Sorry I was feigning idiocy for jokes and to help any fish who stumbled on here to keep making mistakes
In all seriousness though:
Traditional poker strategy holds that the hands you call with should be stronger than the hands the opener is raising with. David Sklansky calls it the gap concept.
Now you may be thinking "what about smaller pairs to set mine? What about suited connectors to apply pressure with when they show weakness plus occasionally flop a disguised monster?"
Yes these are valid reasons to call but they are basically exceptions to the gap concept rule. You only make that exception because you have a strong read that this opener is liable to make the postflop mistakes required for your plans to succeed. Some players are simply too good and too tough for basic cookie cutter ploys like set mining to work profitably.
When your hand strength relative to opener's raising range is weak you are reliant in implied odds or fold equity to make your hand pay. You can't play it for straight up pair value.
When we apply the gap concept to overcalling we have to consider how the caller(s) between us and the opener are going to affect our implied odds and our fold equity. So it is player dependent, there is no set rule for how the gap concept is applied to overcalling.
However, we can use the gap concept to work out in each case what we should do. Firstly if the caller(s) are tough players and the opener is a tough player then the basic gap concept applies and you need an even stronger hand to overcall than to call with. Why is that? Well the opener and callers aren't offering good implied odds and they aren't offering tons of fold equity either - they are good hand readers, they know everyone in the hand are good and they are going to deploy balanced, defensive ranges to protect themselves. The presence of more than one such player inevitably decreases overall fold equity even more than if just one were in the hand but additional tough players don't increase implied odds that much while if you do gii coolers will be a frequent occurrence.
Now, if the opener is a huge bundle of implied odds who opens a tight range and refuses to fold over pairs and a tough player or two already called you may be quite happy set mining along with the other tough players. Your position and your awareness of their likely plan will enable you to possibly avoid getting cooler ed set over set for hundreds of big blinds. You aren't going to call SC though since opener is bombing flop and callers won't continue without cracking his over pair - you won't get odds to draw so unless you flop the nuts you are folding.
Conversely if the opener is weak tight and a tough player already called then you may not want to set mine or call with speculative hands (since the caller is calling with strong hands AND some speculative hands and will be aware of what you are doing with your overcall). Your plan to bluff out the opener will get you into a reg war with the tough caller andealt hough you may occasionally catch eithe player out with a set your implied odds arent great. Instead you might prefer to flat a very strong range but utilise a wide and polarised 3betting range.
If the opener is tough but the callers are calling stations then your implied odds are high and the stations' calls postflop will potentially price you in to your draws. The tough opener will have to reign in his bets for protection or risk offering high implied odds. Therefore you can call some speculative hands. However you want hands that can make the nuts rather than second best hands. Nut flushes and straights and big sets are going to be strong money makers but small two pair, sets, idiot ends of straights and small flushes will frequently get you coolered in massively multiway pots. Same goes for limped pots to an extent.
So it really isn't as simple as "more players in the pot = overcall a wider range". It all depends....