Consider Propositional Lax Logic ($PLL$)

- https://www.uni-bamberg.de/fileadmin/uni/fakultaeten/wiai_professuren/grundlagen_informatik/papersMM/pll.pdf

The Hilbert system of $PLL$ takes as axiom schemata all theorems of (or a complete set of axioms for) the Intuitionistic propositional calculus plus the modal axiom schemata $\bigcirc R, \bigcirc M, \bigcirc S$ below. The inference rules are Modus Ponens and the rule "from $M \supset N$ infer $\bigcirc M \supset \bigcirc N$": 

$$\text{Axiom} \bigcirc R: \hspace{0.5cm}M \supset \bigcirc M$$
$$\text{Axiom} \bigcirc M: \hspace{0.8cm} (\thinspace \bigcirc \bigcirc M\thinspace) \supset \bigcirc M$$
$$\text{Axiom} \bigcirc S: \hspace{0.8cm}(\bigcirc M \land \bigcirc N) \supset \bigcirc(M \land N)$$

A proof of the modal collapse (We can derive both $\bigcirc M \supset M$ and $M \supset \bigcirc M$) of $PLL$ obtained by adding the Excluded Middle (EM) and $\neg \bigcirc false$ was given in this answer: 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?