Public safety vehicles would only have 1 antenna each if this was a real issue....
I don't understand what you are saying.
Public safety vehicles will have as many antennas as they need. Just take a look at a California Highway Patrol vehicle. They'll have 4 or more antennas on them. Spacing is key, also they tend to use high end radios that usually have really good receiver filtering, not the low end stuff that scanners or amateur radios have.
Our PD cars at work have an 800MHz antenna mounted on the roof top, behind the light bar and a VHF whip on the trunk. The separation is plenty to not be an issue. VHF radio is running about 80 watts. 800MHz is running about 15 watts.
We would not have stuck the antennas side by side with only a few inches between them. We spread them out as much as we can.
With good filtering, like between a low band radio and a uhf radio, the issue is lessened by having good filtering in the radio to reduce out of band RF. That helps reduce any crap coming out of the transmitter and will reduce some incoming RF if it's outside the passband.
The trouble with a scanner is they have a very broad band receiver, so filtering won't work. The receivers are pretty wide open to overloading, desensitization, and even damage if the transmitting antenna is too close.
With a CB, it usually isn't an issue since they are often running well under 4 watts. Figure in feed line loss and if you are getting 2 watts out of the antenna, you are doing pretty good. Now add in feed line losses between the scanner antenna and the scanner, and the amount of coupled power getting back into the scanner is even further reduced.
When you are running more power with lower loss feed line, this can be a bigger issue. Especially amateur radio operators or public safety radios running 50 - 100 watts.
If you are referring to the 4 antennas arranged in a square that you'll see on some police cars, those are receive antennas for LoJack, and not transmitting antennas.
But hey, you do whatever you want. I'm just passing on info the OP so he doesn't create any issues for himself.