Do two replacement effects that both try to replace the same event apply in any order?

When two or more replacement effects would modify the same event, you don't apply them simultaneously. Instead, the player who would be affected — or whose permanent would be affected — chooses which replacement effect applies first (CR 616.1). The chosen effect modifies the event, and then you check whether any remaining replacement effects still apply to the modified event.

Crucially, each replacement effect can apply only once to a given event (CR 616.3). So after the first chosen effect reshapes the event, you re-evaluate whether the second effect can still apply to the new, modified event. Sometimes it can (and gets applied second); sometimes the modification makes the second effect no longer relevant.

The choice of ordering belongs to: (1) the controller of the permanent or player being affected, if the effects originate from different sources; or (2) the player whose turn it is (active player) if there's still a tie in determining who chooses (CR 616.1d). Importantly, the game only has a single modified event as output — not two separate replacements stacked independently.

Concrete example: A player would draw a card while both Teferi's Puzzle Box (each draw becomes 'put hand on bottom, draw that many') and a 'skip your next draw' effect apply. The affected player chooses which replacement applies first. They might apply the skip effect first (no draw happens), making the Puzzle Box effect moot, or apply the Puzzle Box first, then re-evaluate whether the skip can still apply to the new event.

So the answer is: yes, they can apply in any order the affected player chooses, but only one event emerges from the chain, and each effect applies at most once (CR 616.1, 616.3).