Although several passages in Berkeley are related to the question whether two or more finite substances can simultaneously perceive numerically identical sensible ideas, it is only in TDHP (247–8) that he addresses the question explicitly and in some detail. Yet, Berkeley’s less than straightforward reply is notoriously difficult to pin down. Some commentators take Berkeley to be endorsing a clear-cut positive reply, whereas others have him giving an emphatically negative one; others hold that for Berkeley there is no fact of the matter that determines an answer one way or the other. I argue that all three readings find some justification at one point or another in the passage, and all hold a kernel of truth. Yet, none of them can be taken unrestrictedly because Philonous’s considered position is disjunctive: either there is no problem at all, or, if there is one (thus warranting a negative reply to the public status of sensible ideas), it makes equally against ‘materialism’ and immaterialism. I argue that the passage can be given an overall interpretation that explains why Berkeley is entitled to hold that there is some truth in each direction. I propose answers to the questions (a) why Berkeley thinks there may nevertheless be a problem after all, and (b) if so, why he can yet legitimately feel entitled to let it rest, that is, why he remains confident, within the philosophical context of his day, that his philosophy does not lead to solipsism.