More players typically means you play fewer hands, within a stronger range, from most or all positions.
Opening UTG with 9 players is going to be perceived as much stronger than doing the same with just 6 players, even though in both cases you are first to act preflop.... Since you have 8 more players to act, rather than 5, you have a much bigger chance of getting 3-bet.
The same is true with a 7- or 8-handed table, just a little less so.
So it’s better to identify positions backward from the button, rather than forward from the big blind, when constructing ranges etc.
Regarding one of the first comments: I would be all in favor of making hold ’em an 8-max game. The idea of 9- or even 10-handed games is a relatively new thing. It seems more driven by casinos wanting to pack in as many people as possible than good play. (No one played 9- or 10-handed when 7-card stud was the dominant game, for obvious reasons.)
To me, 9- or 10-handed games are less appealing, in that it allows players to sit back and wait for premiums and not have to deal with more ambiguous/tricky decisions. Limiting hold ’em to 7 or 8 players means a little more action, a bit more variety, and should requires some more skill, IMHO.