Our chief has made TQ mandatory for every officer and put a full trauma kit in the glove box of every police vehicle (SOF-T, Quickclot, Izzy, extra gauze, chest seals, shears, tape, gloves). It's not expensive either. We do shift training once a month in tbeir use. If any officer wants to propose the same, make sure you have full price quotes and a per vehicle price if you want the suggestion acted upon. We bought seperate components and sealed them in heat sealed evidence bags with nips cut in edges to aid in opening. Cost less than any complete kit. Plus it is good PR when he can tell city council about their use in traffic accident victims, etc.
As for the other peoples questions about multiple gunshot wounds or other injuries...
All serious wounds to extremities get a TQ first. Everything else for an extremity is icing.
All junctional wounds that do no intrude into abdominal cavity but are too high to get a TQ get Quickclot/gauze. (Shoulder, hip, etc.)
All chest wounds get a seal.
In that order and as a general rule.
In general, you don't stuff gauze into central body cavity. There is nothing to pack into or against. Combat gauze in an extremity is used when a juncture wound is done or not present and there is some left for extremities, otherwise just regular gauze. Pressure dressing is last. Direct pressure is best, but if you have to hold one wound and there is another that needs pressure, or you need to move the person, a pressure dressing is nice, but not necessary.
A mini kit like the CLEER on my carrier can handle one basic of each injury. Chest seals come in twos so covers both sides entry and exit, plus you can make a makeshift seal from tape and the packaging material.
A full kit can cover a very bad or second wound with extra gauze, but still not enough for some situations.
Then there is the situation where you come across a downed fellow officer from another agency, with no medical gear, in something like an active shooter scenario, but you can't hear any gunfire or screams to direct you to any emergency. Do you stop and use your only kit on him? Do you just leave him there to die to keep looking for a threat? Do you toss him your IFAK and go look for the threat with no IFAK? Much easier decision when you have a spare to throw down and can keep moving with the other one still on you.