Is it possible to run multiple patch type antennas through the same receiver input?

 

Yes, BUT.
They may interfere with each other, so there may be no advantage.
Each Antenna also contributes a certain amount of Noise into the mix.
There may be other undesirable "Combing-Effects", rather than an even gain in all desired directions.
If you need a larger coverage area it's best to design an Antenna specifically for the application.

What are You trying to accomplish ?
Sounds like FPV Goggles.
.
.
.

 

You can combine identical antennas to one feedline. The phasing cables would have to be specific to the frequency in use and cable type specific impedance to match the antenna to the receiver impedance.
In some cases, you can use a "combiner" (opposite of splitter) to combine two antennas into one feedline.
Article about phasing antennas with coax:
https://www.qsl.net/dk7zb/Stacking/coax.htm