It depends (but probably not).

Some forms will be achievable, with more or less difficulty. Any form? No.

There are several limitations you did not take away (some of them are discussed in the Sight of Proteus (Behrooz Wolf) series by Charles Sheffield, where an intentional transformation machine, the "form-change vat", is a plot device):

• conservation of mass. You cannot become a bulldog twice as big as a man, since you'd also need to become half as dense as a man - your mass cannot change (you might be able to take in some water as ballast).


• conservation of chemical species. Bones require calcium; there is between one and two kilograms of calcium in a human body. If you want to grow bony armour, you can't do so using calcium, as there is not enough of it.


• "square–cube" law - your organs, bones etc. must be able to handle the stress (for example a femur twice as long would need to have half the cross-section to maintain the same mass; this would make it twice as likely to break per unit length, and eight times as likely to break overall).


• the target organism and all intermediate forms must be survivable. You cannot transition from a human being to a fish, unless the transition is so short that you can literally hold your breath (actually blood oxygen levels) while it takes place. You need to mutate into an amphibious life form first.


• metabolism requirements.

Also, the target and intermediate forms must be able to sustain a human brain in more or less unchanged form - otherwise, the "control" would vanish as soon as the brain changed enough.

There are also subtler difficulties:
- to be able to do something is not enough, you need also the knowledge about what to do. As discussed with @ShapeOfMatter, you might redesign your bones to make them stronger while using less building material - a thicker cortex with trabeculae organized in tetrahedral lattices along stress vectors; but to do that you need to not only know Wolff's law but also make very precise estimates of the stresses of a structure that does not exist yet (or do it slowly through trial and error over a period of many weeks, if not months).
- not all body material is actively remoldable (hair, nails, teeth enamel). That will need to be discarded or digested and recycled, which requires temporary specialized cells (that you don't have and must make on purpose).

Short version : No.

Would they be able to transform to another creature, and regress at will if they wanted to? Say this person transforms from human to a bulldog or something twice as big as a human

Your problem are essentially two key things :

Physics

Physics doesn't let you just suddenly generate energy (or equivalently mass). So let's say you want to convert to something one kilo less than are, that means converting the one kilo you loose into energy and letting it go away. That's nuclear bomb levels of energy every time they transform. The converse also applies : transforming back from something one kilo less to your original state will require you to suddenly acquire all that energy back, which is even harder.

Just one gram ...

It's probably worth noting that for the "Little Boy" bomb dropped on Hiroshima, the core was 64 kilograms but only 600 mg ( less than one gram ! ) was actually converted to energy. Little Boy was a 15 kT nuclear weapon so your shape-shifter losing one whole kilo would be equivalent to about a 1.7 Megaton nuclear weapon. I wouldn't want to be nearby when they change !

Physics is a cruel mistress and she's real fussy about converting mass to energy and back.

Biochemistry and life

The other problem is "to another creature". Making you look from the outside like another creature of the same mass is doable, but if you start changing cells and their operation then you start dying. Those cells have specific functions and they connect together into a complex biochemical machine that does not work when you start changing things like cell behavior.

We have names for various changes in cell functions as you describe : they are serious illnesses.

The term "person"

Who exactly is "you" and how do you maintain "you" when you change everything else ?

Your psychology and your body and connected by the biochemistry of the whole gizmo. Becoming e.g. a horse at a cellular level, means you no longer have the functions that knit together to make a human.

But even if all I change into is another human, that's still a problem.

I have a lot of things I have learned to do and expect to happen in a particular way. My coordination, movement and muscles are things I have learned to expect to do certain things in certain ways. When they don't perform as expected, you do things like trip, stumble, fall over, fail to catch the ball thrown to you, don't pick things up properly and so on.

Anyone who has had an injury that changes their movement capability permanently will know what I mean. I suffer from an ongoing knee problem I developed in my forties. Buy my brain learned to do things and it's hardwired ("muscle memory") and very hard to change without conscious effort. I still find myself absentmindedly trying to e.g. take two steps on a stairs ("the normal way") rather than the "one step at a time" approach I need to avoid pain and falling. You adapt a little over time (a long time) but the old "instincts" are still there waiting to (literally) trip you up. You'll e.g. stretch your gait too far (but it wasn't too far for thirty or forty years, but is now). You'll see that bus nearly ready to leave and instinct will say "run before it leaves", but one step will explain why you're not actually going to be able to do that.

You shape-shifter will find themshelves suddenly in possession of a set of limbs which don't work as expected. Their brain issues instructions they can't match and pretty soon your shape-shifter is face-planting and falling all over the place.

It's a bit like being a new-born. It takes a long time to learn how to use those legs and arms and keep your balance and you go very slowly from "helpless as a baby" to "ballet classes" :-). You take it for granted when you've been doing it all your life, but for your shape-shifter it's a whole new ball game every time. It's going to be very, very bad.

Frame challenge

If a person had control of every single cell of their body ...

There's your problem right there:

(1) Estimates put the number of cells making up the human body at around 30 trillion. No 'person' could hope to control (or even comprehend) that number of cells.

(2) Humans contain a similar amount of bacteria - perhaps 40 trillion - mostly in their gut. They are not part of the body and therefore not controllable by your criterion.

(3) Even if you were able to change your body to look like that of, say, a sheep, you would be a bald sheep because hair is not alive. Even if your cells were sheep cells, it would take months to grow any kind of a fleece. Similarly with hooves and ram's horns.

(4) Tooth enamel is not made of cells. Your old teeth would have to be rejected, but then you have to form new adult teeth of the creature you changed into.

(5) The hardened part of bone is dead. Destroying your skeleton and creating a new one would take years during which time you would be completely incapacitated.

(6) Your knowledge of biology would have to be greater than any person ever to live, in order to correctly 'build' a creature of a different species. Most people cannot correctly draw a dog let alone create a fully working replica of one.

(7) Your brain would not fit into most creatures. If you changed your brain, you would lose all your memories and skills.

(8) About 100 other reasons...

Conclusion

Unless you are pretty much omnipotent and omniscient (i.e. a god) you have zero chance of doing what you are asking for.

With the current constraints, yes they could. Assuming that the control remains if their brain capacity reduces.

For those thinking of a rapid transformation within minutes or days, that's not going to happen: https://youtu.be/CLY-FMxsb2U

The catch is the time and energy it takes to transform. It takes an awful lot of energy to change your body in a relatively short timespan, and "relatively short" is already measured in weeks and months. Look at the growthspurt or baby growth for example. And that's when the body does the planning for you!

There is also the matter of staying alive during transformation. If your heart or bloodvessels aren't finished yet or finish too quickly, you are going to have cardiovascular problems. Or if you haven't prepared a decent layer of fat for the energy and material to transform and you are changing your limbs causing you to have limited ability to get or eat food, you'll likely starve yourself with your own transformation.

Needless to say, any transformation would need to be meticulously planned and prepared for, from the food you eat to the time it takes to the likely capabilities you have at certain points to what shapes you have in the meantime so you don't kill yourself with nerve/bloodvessel problems. It's probably best to check in a hospital and let them help you with intravenous food and going to the toilet for the extensive amount of extra waste you are going to produce...

There is a widespread natural process to transform into another creature - pupation - and most insects do it. However, the larva dissolves itself completely, including whole nervous system and grows again from stem cells. It indicates clear evolutional advantage in growing new body from scratch instead of trying to morph existing cells in place.

This is probably not what you want, the person doing it would die in the process. Preserving the brain alive is nontrivial, it needs quite involved supporting structure, not to mention reconnecting it to new body. With this in mind there are some options:

1. Old body is kept alive and new body is grown on it. Only when new body is self-sufficient, then the old body is shrunk or discarded except for the brain. This means the old and new body must be fully biologically compatible.




2. Brain is kept alive by some external, natural or artificial, support system umbilical, while the new body is being grown around it.




3. Some way to transfer the consciousness with memories into newly grown brain. Most flexible but requires much deeper understanding of biology than former options.

No, our body is too complex to change it in a way to be able to survive it.

With a needle and a steady hand (or with an ISO image file and a hex editor) you can theoretically change any bit on a DVD. Does this mean you can take a DVD containing the latest version of Windows, and change it to contain a working Linux installation DVD? Or change it to a DVD with the latest Avengers movie on it?

Being able to change any byte doesn't mean you can do it.

Being able to change any cell doesn't mean you can create a functioning lifeform.

Your job would be even harder than my example with the DVD, because the DVD doesn't have to be kept "alive" during the operation.

Yes, absolutely!

Embryology starts with a single cell that can transform to whatever complex life it is programmed to become. This process can of course be restarted, e.g. salamanders regenerating lost limbs etc. At the same time controlled cell death is part of every day normal maintenance in all living things.

The only thing you need to control is your DNA. The DNA will control everything else including the things you mention. There are many possible ways to alter DNA. For example:

• Highly efficient gene editing viruses


• Nanobots


• A very precise radiation device


• etc.

Viruses and nanobots could be stored externally (pills/syringes/cream etc.), or internally in biological compartments and released at will starting the DNA editing and subsequent transformation process.

The transformation would need some time though. The longer the more realistic. Months, weeks or days. If the transformation need to happen in hours, or maybe even minutes, you are starting to push the speed of biological processes into their theoretical limits.

It would of course be impossible with any foreseeable technology due to the complexity of it all. But there are absolutely no theoretical limits saying it is not possible. Below I will address some of the other points that has been brought up in other answers:

Physics / conservation of mass etc.

If you are increasing mass, eat more during the transformation process.

If you are decreasing mass, leave mass behind. Your body could self amputate your human legs and instead you would grow smaller bulldog legs. Or maybe liquefied cell waste would be expelled through the skin or an existing orifice.

conservation of chemical species

If you want to grow bony armour, eat something containing a lot of calcium.

"square–cube" law

If you are turning into a dinosaur, grow larger bones.

the target organism and all intermediate forms must be survivable. You cannot transition from a human being to a fish

Grow your gills at the same speed you degenerate your lungs. Submerge yourself so your gills receive water, but keep breathing air through a straw at the same time.