I know this post was old, but I think it is still relevant.
I didn't test this, just a theory. I saw some older posts asking. I thought this would be easier than some of the suggestions. I'm not sure if anything in C3 was adjusted for that, but here is a possibly solution if not.
You can use an invisible object and pin character to the object.
The invisible object can have 4 or 8 frames that change depending on what direction the player is walking. A frame change can change the bounding box.
32x32 in a 32x32 is a tight fit. Set bounding box to 30x30 and align it to center-top of invisible object when moving up. The character will stop properly when moving up and it will leave room on sides.
Center-left when moving left.
Top-left if moving up-left
Etc.
The bounding box will change depending on which way the character is moving, but it will still leave room on sides to prevent accidental collision.
It should allow movement between 32x32 tiles and should make it look pixel perfect.