In most cases, allowing multiple attempts is a poor idea. If you'd let every character try disarming that trap, why would you not let one member in a party of five try it five times? In other cases, you can allow multiple attempts regardless of the amount of people, such as breaking down a door. In some cases, like attempting to discern someone lying, a larger group has a natural advantage, and I feel that it makes very little sense to try to artificially remove that. If you started fiddling with that, you'd also have to compensate for the natural disadvantages a larger group has, like difficulties fighting in close quarters, loot being divided to more people, etc. They also have more advantages, for example they can have more casters meaning they get more spell casts per day than a smaller group would, but it doesn't make any sense that their mages would be any weaker just because there are more than one.
In most cases, if you feel the need to balance the campaign to account for a larger group size, do it by adding enemies, forcing them to fight in close quarters, using AoE spells and abilities against them, or adding other obstacles. Don't do artificial difficulty hikes. RPGs are made to model real life at least to an extent and changing DCs just to make things harder is defeating that purpose. Always remember that you're running a fun game, not a tabletop version of Dark Souls or a lesson in statistical mathematics.
To aid this, I often run my campaigns with the idea "does this make any sense?" What it means is that let's say my player wants to do something that has no direct rule, but that makes sense within the context of the game and there is at least a theoretical possibility of success. An example off the top of my head was a large half-orc character wanting to throw a very small-sized (half-?)elf over the enemy battle line to wreak havoc from behind. Now, I could just say "no, you can't do that" because there isn't a ready-made rule for that or a convention on what the skill check should be, but instead I chose to allow them to try, the orc was strong enough that he could, at least in theory, easily throw the small elf over the heads of the goblins they were fighting. It makes sense, therefore I have no reason to not let them do it. I cooked up a roll on the fly, making the orc roll throw with some penalty because he was throwing something a lot bigger and heavier than a javelin or a rock, and the elf roll a landing with some penalty since she wasn't in control of her trajectory. I could easily have told them no, but instead it became one of the more memorable moments of that dungeon.
TL;DR: If possible, let your players play with as few limitations and artificial difficulty hikes as you can. The gameplay is a lot more entertaining and it will be a good exercise for your creativity.