So I play minecraft on ps4 on a server that has 4 ppl in it at all time. I built I'll mangoes mob grinder design up at build limit and over an ocean. When the host uses the grinder by himself and no one else is online he says it works perfectly but when I use it and other players are online I get no drops plz help. I think the other players are taking up the mob cap.
The problem is twofold. Mobs will spawn around other players on a server, and mob spawn attempts start at the bottom (Y0) and go up until they succeed, so mobs will spawn at lower Y elevations before spawning in your sky farm. This means when other players are online mobs are unlikely to spawn in your farm.
Assuming you got other things right (which is unknown since you provided no details) then your best bet is to try and AFK at your farm for a while in the hope that there will be a period with no other players online.
Your other option is to build the farm as low as possible, which will require you to eliminate all other potential spawn locations around your farm. Since I play the Java version I'm not sure if spawning rules are the same on PS4, but for Java Minecraft mob spawns need to be blocked in a spherical area with a radius of 128 blocks from your position (I usually just go 8 chunks in every direction around the farm).