A proof of the modal collapse (We can derive both $\bigcirc M \supset M$ and $M \supset \bigcirc M$) in a certain Intuitionistic modal logic was given here: https://mathoverflow.net/questions/296440/modal-collapse-upon-addition-of-the-law-of-the-excluded-middle-to-an-intuitionis. 

The modal collapse was claimed in  https://www.uni-bamberg.de/fileadmin/uni/fakultaeten/wiai_professuren/grundlagen_informatik/papersMM/pll.pdf:

>"...if we add the axiom of the Excluded Middle (EM) and $\neg \bigcirc false$ which is valid for both $\Diamond$ and $\Box$ to the modal system $\bigcirc R, \bigcirc M, \bigcirc S$ then $\bigcirc$ becomes trivial. We can derive both $\bigcirc M \supset M$ and $M \supset \bigcirc M$
In other words there is no classical Kripke semantics for $\bigcirc$." (p.4, para 1 of the above article)

However, I was wondering 

(1) Can we get the modal collapse if we only assume the law of the excluded middle, and we don't assume $¬◯⊥$?

(2) If we are able to avoid the modal collapse by abandoning $¬◯⊥$, would abandoning $¬◯⊥$ be problematic in other ways?

(3) Does the proof of the modal collapse go through if we adopt a classical multiplicative linear logic? (i.e, if we abandon the structural rules of contraction and weakening (as in the proof system presented here: https://math.stackexchange.com/questions/2395602/a-sequent-calculus-proof but treating $\rightarrow$ as primitive, and not as definable via other connectives, as it usually is in linear logic)