Category URL: Parent Child Category in same url

Thank you in advance to any help offered.

I have two sections of my website setup as categories; both of which have identical child categories.

Let’s say category 1 is males and category 2 is females. They both have all the same child categories. Let’s say they both have child categories of: height, weight, and eye color.

The link for Parent Category 1 (male) is https://www.domain.com/?cat=25
The link for Parent Category 2 (female) is https://www.domain.com/?cat=26

The link for Child Category 1 (height) is .com/?cat=30
The link for Child Category 2 (height) is .com/?cat=31

Here’s what I would like to happen:

When I click the child category Height under Category 1 I want the link to include both categories. I want the link to be: https://www.domain.com/?cat=25&cat=30

Following the same logic on category 2 it would be: https://www.domain.com/?cat=26&cat=31

I imagine it is possible through custom permalinks but I would like to do it without that whereas I don’t want to affect any other links on my site.

Is this possible?