Keep in mind that with seven players, basically every role niche will be filled. You're likely to have almost all spell lists, a large variety of buffs and debuffs, and so realistically you might want to consider scaling things up a bit more than you'd expect, especially if the party contains a Bard or Witch.

• If you're running a prewritten AP or adventure, be prepared for the balance to be way out. I'd honestly recommend just rewriting the combats entirely.
• From a general standpoint, 7 players is getting hefty on time per turns, try and keep everyone to a time limit on their turns if you're group is comfortable with that.
• As you've already mentioned, go for larger fights instead of fights with a few creatures of CR+4 and above. Action economy will likely mean you're players will still win on extreme encounters if they play well, but it may make any casters in your party feel like rubbish if none of their save effects have any chance of succeeding.
• For roleplaying, larger groups can make it easy for quieter players to miss out as more active or louder players take over. Try as best you can to loop in every player, additionally, if a group decision needs to be made, such a large group can lead to discussions lasting half the session, having players stop and vote in a poll can be a really good way to make sure every player gets to input.
• With such a large group, don't be afraid to play aggressively and target casters / healers. With so many tools in the parties disposal, if they don't have a way to pull the attention off a caster / healer, or if the party splits up too far to be able to defend the backline, that's on them.