Unfortunately no you can only have 3 kill streaks equipped at a time.
3
Because in C.O.D MW3 all of your kills count towards kill streak rewards. For example if after you killed the right amount of people to unlock the pred missile you can unlock the next award in your kill streak set with kills gained from using the Predator missile. Hope I helped.
By Completing challenges
Your fourth kill streak slot is for killstreaks aquired from care packages.
a moab is a 25 gun streak only 24 with hardline, which means you can't use killstreak rewards to get a moab in mw3 but in mw2 you can
To get the title 'toxic'in mw3 you must be killed by an enemy MOAB. A MOAB is a giant bomb you get in mw3 for getting a 25 kill streak. Or 24 if you are using the perk Hardline
You have to use the assault strike package in order to get it. (it's a 17 kill-streak reward)
you have to get a 25 GUN streak preferably using specialist package so you have no kill streaks and with hardline 24.
To get M.O.A.B (a.k.a a nuke), you have to get a consecutive kill streak up to 25 kills, or 24 if you have hardline. You also have to have the specialist or assault strike package, Remember, if you use assault strike package, your kills from killstreak rewards e.g reaper count towards the nuke, or M.O.A.B.
100 bullets kill a juggernaut
Makarav
Kill kill kill !!
Get all 3 killstreak rewards within 20 seconds