I know it'd be against the lore but I'd completely be in favor of rectoning that and make cross breeds instead of just ''take mother's race'' which in my opinion is kinda silly.
If you have half-breeds, then you'll inevitably have half-half-breeds, then half-half-half-breeds, etc. Everything would stretch so thin that it'd dilute the races, which would defeat the purpose of having distinctive races. Especially in a world like Nirn where everything isn't based on "human", but also elves, orcs, cat people (ostensibly elves, who already range from house cats and battle lions, to nearly-human in appearence), lizard people, vampire snake people, fox people, and sloads. I seem to recall a book mentioning a navy fleet that included dog or rat-like people, but I can't find it (might have that mixed up with something else).
We know orcs and elves are capable of breeding with humans and each other, and if Khajiit are related to elves, you could include them. If we accepted the others are capable of interbreeding as well, that would make a real mess of everything.