I think we have demonstrated that our collective ability to imagine exceeds our physical form.
Consider the following creature:
It's a social creature with a very rigid role based hierarchy. It is a predator, and the sneakiest of predators. It sets a trap and quietly lies in wait for unsuspecting prey to go by. The predator identifies what the prey wants to see, and constructs an on-the-fly bait customized for this individual prey. If the prey sees the bait, and begins to fall for it, this predator carefully adjust itself so that it looks like there is nothing else in the world but the bait, and that no one else in the world could possibly get it. It's the perfect morsel for this prey. When the prey gets too close, SPLAT the prey is reduced to nothingness in moments by acid. Even if a prey escapes to tell the tale, nobody believes it because they never seem to be able to compare notes. After a failed attempt, it looks like no attack occurred at all. This is, in fact, why the creature is social. Success or failure, it rapidly disseminates knowledge of the result of the transaction to others of its cluster, all of which have specialized processing nodes which ensure any inconsistencies in the attack, which might help the prey outwit the predators, are smoothed over so that noone ever is the wiser.
Sound fantastic and potentially an exotic creature? I envisioned it right here and right now. It's also a SQL server. We deploy hundreds of them every day around the world. You can get a degree in managing them, if you want.
Chalk one up for imagination.
If a creature is advanced enough, its mind is going to be more important than its body structure. Thus the real challenge for making an "alien" alien is to create an alien feeling mind. To me, mathematics is in an excellent position to posit the ability to create such a mind. We have a long history of creating mathematical languages which can describe fantastical facts which had never been imagined before (complex numbers... seriously?). Thus I expect we would create a language describing fantastical creatures, and then use the simulation to build all of the "fine details" that end up actually creating the alien feeling mind.