All you can do is to play your hands big hands for value. If it's early in the tournament and stacks are deep or over 100+ BBs, then you will get a number of callers calling your raise PF with a wide range of hands, looking to hit big and take a big pot. In the early stages of an MTT, you'll find either players opt for a loose/wide call range when blinds are deep or for more a tight, survivalist approach to the game. Both have their pros/cons.
I think of your problems is your opening raise size. Raising it 10-15x BB isn't screaming "fold, I have a big hand." It's saying "I have a big hand, come and crack it!" You're really polarizing your range if you're raising huge with your monster hands and limping/standard raising with your other hands. If your opponents know that you have QQ+ when you make it 15x BB, they can call with a lot of hands and probably feel confident they'll get paid off when they do hit.
Another problem is that you're building this huge pot preflop, which is great when you do win the pot, but it makes it a bit harder to continue betting without committing yourself to the pot. The bigger the PF raise and the more callers you get, the bigger your future bets will be compared to if you had raised 4-5x BB.
To give an example, lets say stacks are 100 BBs deep. If you make it 15x BB with AdAc preflop and get 4 callers. The pot is now 60 BBs and the flop is 7s 8s Jh. You all have 85 BBs behind and you're first to act? How do you continue here? You could very well still have the best hand, but there are a lot of other hands your opponents could hold that can outdraw you. Also, hands like 77, 88, and 910s are also in your opponents range and have you crushed.
You can either check it down and maybe get to a cheap showdown. Or maybe bet out and hope to pick it up, but how much can you bet out without committing yourself to the pot, but is also enough to maybe make the weaker hands like 55, 66, KQ to fold? The pots already 60BBs, so if you bet out 40BBs, you leave yourself with 45BB behind. Almost half of your stack is in the middle. What's the plan if you get 2 callers and the turn is a brick? With over 50% of your stack in a pot of 140 BBs and 45 BB behind, are you check-folding the turn? Or do you commit the rest of your stack is you check and someone shoves? You can fold and still have 45 BBs which is still plenty, but it can be hard to let it go when you have 50% of your stack in the middle.
In my example above, the bet sizing might be terrible, but i just wanted to illustrate how pots can get really big when you're opening for large raises preflop and getting multiple callers.
Now, lets say its the same scenario as above but this time you make it 4x BB. The pot is now 16 BBs and flop is 7s 8s Js. Now your the pot size is much smaller and you don't commit as many of your chips when you're betting. If we made the same 2/3rds pot size bet as above, or bet out 11 BBs on the flop and get 2 callers, we still have a lot of BB behind. So, we can easily opt to check the turn card and maybe call a smaller bet, then re-evaluate on the river. Or, if an opponent decides to make a huge bet after our turn check, we might decide our hand could be beat on that board and with hands like 77 or 88 and we can fold and still have 80+ BBs behind.
So, as far as your raise sizing should be, if you're in early position and during the early stages, make it between 3-4x the BB. And in the mid-to-late positions, make 3-4x +1 BB for every limper. So, if you're in late position and there are 3 limpers before you. You might raise it 3.5x BB + 3 BBs (limpers) for a total of 6.5 BBs.
I want to add that making your opening raises a bit smaller allows your opponents to come over the top of you with their big hands. So, if you're raising 4x BB in early position with a range of 88+, your opponents might 3bet you preflop with wider range, which is great if you have QQ, KK, or AA as you can 4 bet them and build a big pot if they have a big hand. Whereas, if you were raising 15x BB with hands like QQ+, your opponents have no reason to ever 3bet you preflop knowing you have a monster. So, they don't have to commit a ton of chips preflop. Just call your 15x raise and fold if they miss.
Now, for post flop play. There are way too many things to consider, but as a general rule that I follow when I play, the more coordinated a board is, the more I proceed with caution against multiple opponents.
So, against 4 players, I might not want to get too involved with a hand like KhKd on a board of 4s 5s 8s because it possible it hit a couple of my opponents very strong. Compared to a flop of 7s 2h Qd, this is a flop that I'm more comfortable getting involved with. It's a pretty dry board with no immediate straight or flush draws and I have an over pair. So, I might get action from KQ, AQ hands that i beat a lot of the time. Not saying that I wont lose with KK on that board, but it's a board I'm more comfortable getting my money in compared to the other one.