Personally I do not believe in double-teaming. I find it boring for starters. If you like to get in to 2v2 or 3v3 brawls all at the same time, that's cool (and more importantly, fair). Find some people that like to play the same way, and play that way.
If you want to create a game with 2 of your friends on mics and play a 3v3 against randoms that have no connection to one-another and will generally find communicating and working as a team difficult due to being triple-teamed and seeing the spawn screen more often than their own reticle because they stand no chance against an efficient, close-knit team that outnumbers them then that's also your call. Although, I for one would find that extremely cheap. Moreover each time you get a kill, it scatters the other team making it more likely to find lone players running about for more 3v1 action. Where is the fun in that? For either team? Where is the skill? The challenge? If I were a newbie, or even around the rank 20s-30s, I'd probably quit and my other team-mates likely wouldn't be far behind. It's an effective way of putting people off of joining your games in future.
If you expect a bunch of people that have never spoken before to suddenly work as a team against eachother when respawns are placing you all over the map, it's not going to happen. You could argue "Yeah but you'd die less if you worked as a team", but that's only true against newer, casual or average players. The truth is that double and triple teaming has more cons than pros unless you have some sort of team strategy and play regularly with those people.
If a team of 3 came across an average Predator minding his own business, he suddenly turns to see 3 enemies 5 feet away about to attack him, he'd probably panic, unconsciously accept he is going to die, and instinctively proceed to try and kill atleast one of you before he gets killed which is not going to happen.
A good player will see an opportunity for 3 kills in quick succession, will understand that you are not dead until you're dead, and that there is a way to turn the odds in his favour IF he makes the right decision and his skill can back up the play that is required by that decision. A good player will have awareness of his surroundings at all times and be moving CONSTANTLY, so no surprise attack for you three. He will run the hell away the moment he sees you and throw sharp objects at you like the Disk or a Spear, or if you're really unlucky just destroy you with the Plasma.
Now, I personally do not use the Caster even if someone else is spamming it at me, and tend to roll with Spear and Disk at all times. For example, In the Refinery or Pyramid with the enclosed hallways, I'ma run away down a corridor and when I get to my cool-down period from the sprint, I'ma jump forwards to keep the momentum WHILST being able to turn, and I'ma throw a Disk or Spear at you (Possibly both if I have the time) before I turn around and run the hell away some more. Three of you in one corridor? The spear is almost guaranteed to hit atleast one of you, and that disk is gonna atleast hit one of you, probably two. If you get to me first? So what? one kill shared between 3 is nothing and there will be less people running about elsewhere to kill my other team-mates. 30 seconds is the most I will need to get my weapons again and be back on the hunt for you. So.. each time I meet you you have a possibility of one of your players getting one kill on me, or me getting 3 kills in a row. Even if I just kill 2 of you before I die, it's a good trade off.. If I kill 2 of you with my weapons, the third is going to want to run because that's when I'll start chasing him.
Moreover when you double-team you have to share the kills with your team-mates.. If you die you have to not only recollect weapons (if necessary) you have to locate your members, rejoin them only to tag around and share more kills. It limits your own potential for kills. If you play competetively then what have you won? The ability to boast that 3v1 you were able to pick them off individually? Nice skills. If you play for fun, where is the challenge? Where does the game stop being simply sitting in front of your TV pressing buttons for the sake of something to do, regardless of what's on the screen, and become something fun, challenging and adrenaline pumping with an unknown outcome?
Personally I love matches where it's me on one team vs multiple opponents on the other team. The advantage and chances of winning lie with me, but it is fun and somewhat challenging. You'd be surprised how many good players actually fail at understanding this concept where less = more, but I guess a good player isn't necessarily an intelligent player lol.
Finally, I will say that if you want to get better at AvP, regardless of what species you play, double-teaming is DEFINITELY not going to get you those results and all you will succeed in doing is effectively running around and pressing buttons for the purpose of killing time.