Consider Propositional Lax Logic ($PLL$)
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: Modal collapse upon addition of the law of the excluded middle to an Intuitionistic modal logic.
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?
A response was given below which I do not understand:
"(1) Clearly not, as the logic is contained in the logic axiomatized by classical logic and ◯A for all formulas A."
I would also be grateful for any clarifications of this comment.