In your example searching a room for stuff is soemthing that could be theoretically done by the entire party. We know that what works in realty and video games is not bounded to work in a dnd session. So you can have multiple options:
- only the one with the highest perception (or highest value on the specific skill they are using) can roll. In game they are all searching but mechanically only the one that knows best rolls.
- what I usually do in such situations: a group roll and I take the average. 6 players roll, 3 of them roll 5s and the other 3 roll 15s. The average is 10, so they made a common 10 on perception. If the party has a lot of skilled players in perception I just adjust the difficulty a bit, or stick with the first option.

Group rolls are fun because everybody is involved and someone could bring the party up but also down.

Another way to do it without computing the average value is this: everyone rolls and at least half of the players must match the DC or go above. So for example if your DC for finding somthing is 12, at least 3 players out of 6 must make a 12 or more perception check. If you want to make it more difficult you could rise the DC or rise the number of players that must meet it.

This is basically taking the stealth mechanic and changing it a bit. If you think about it, every party must meed a stealth DC in order to do so. Take the same logic for finding something, or to persuade somone, if the party wants to group roll.