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 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.