Maximum number of combinet object

[Pigowallace]

Hi everyone,
I am new to the forum and I hope to find a solution to my problem.

I am working on a sheet that could allow me to find the maximum number of combination starting from 3 possible objects which must be consider together.
Basically each "final group" the group is made up of one Obj1 and one Obj2, which have to be coupled to one Obj 3.
The final "group" is a couple made up of:
- One Obj 1 + One Obj 3
- One Obj 2 + One Obj 3

In addition to this, there are 3 possibile categories of each object that can be coupled together.
In the simple couple, each Obj 1/2 must be coupled with a Obj 3 of the same category, but the final group can be create between different category.

For example:
- OK:
--- A + A
--- B + B
- Not OK:
--- A + B
--- B + C

I leave here a table with some datas.
Do you think is possible to automate the process?
Maybe with and indication telling which are the coupled items (for example: max combination = 150 with 100 A+A/B+B and 50 B+B/C+C)

Thank you

	A	B	C
Obj 1	92​	668​	756​
Obj 2	560​	496​	680​
Obj 3	752​	1436​	444​

TL;DR:
- I must have at least one "Obj 1" and one "Obj 2" in each "combination"
- Each Obj 1/2 must be coupled to an Obj 3
- Obj 3 must be of the same category of Obj 1/2
- The final group can be created between different catagories