Combining matrices in a function

I have a 3x3 cell. Each element represents the vehicle(s) ID number of a house (a house can have one or two vehicles)..

The house A can have the following vehicle combinations.

A={173 [173,178] [173,180]

[178,173] 178 [178,180]

[180,173] [180,178] 180}

I want to combine with cell B which looks the same:

B={173 [173,178] [173,180]

[178,173] 178 [178,180]

[180,173] [180,178] 180}

So that I then have a 9x9 cell with all the possible combinations. House A and B cannot have the same values e.g. {173;173} not allowed

Later I want to combine A and B with house C (C is the same 3x3 cell). And later A,B and C with D (D is the same 3x3 cell).

A,B,C,D has an equal 3x3 matrix with values that expresses the impact the vehicle(s) has on the house called VehicleA, VehicleB, VehicleC

Is there a way to make a function that combines matrices like this?