can transmutation magic be used for a person to temporarily shapeshift?
Yes it can.

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can transmutation magic be used for a person to temporarily shapeshift?
Yes it can.
In your if’s world, is the enlarge/reduce spell from the transmutation school a thing? How about “invisibility”? We reduce the bear’s size, cast invisibility on it and
Unfortunately Anon, there is no one to one comparison with D&D spells. As for something comparable, likely not. I've mention before but when transmutation mages change objects they can only change objects into things of simmilar mass. The same rule applies to shapeshifting which is why despite transmutation being the most common magic school, shapeshifter mages are quite rare.
So if one were to just enlarge or reduce the size of something the mass wouldn't change with it, which would be very problematic in a lot of instances. (especially if using it on something alive)
We reduce the bear’s size, cast invisibility on it and
I see where you are going with this Anon, but it wouldn't work with this magic system. So no mini bear. The invisibility might work to get it into the palace, but MC is probably not keeping it out of Igor's notice for long.
could a Transmutation specialist shapeshift?
Yes! They would have be a really adept trasmutation specialist, but it is for sure a possibilty. Actually, Sentinel mentions mages who use magic to shapeshift in the last update! (It's a throwaway line in his who speech, so easily missable)