Admetus can have many different relationships with many different cats. Here are some of the few cats he could be related too.
If you haven't noticed how much time Admetus spends with the Jellicle leader, then you are surely blind.
As far as I can tell, Admetus does not spend a lot of time with any other elderly tom except for Old Deuteronomy. Now, we all know that Deuteronomy is loveable but at the same time we do not see his closeness with many. However, he shows it with Munkustrap, Tugger, Mistoffelees and Admetus. He sits with him during the Jellicle Ball and during most of Skimbleshanks' song until they make the train. Plus, the old, loving tom seems to enjoy Admetus' company greatly! Just look at the two of them and tell me that just doesn't melt your heart!
Asparagus may not appear in the stage production of CATS but Amdetus doesn't always star in the stage production as well. (Even though he should.)
Asparagus and Admetus hardly interact. However, Asparagus does spend a lot of time with Jellylorum. Since Admetus is close to Jelly, there is a large chance that Asparagus could be Admetus' father sicne Jellylorum is close to him and seems to be his mate.
Also, on another note, there is this really cute scene after Grizabella leaves and Bustopher enters where Admetus puts his head through Gus' arm. Here's the screenshot
Jelly and Admetus have similar patterns in their fur and spend alot of time together during the movie. When Mistoffelees' is performing his number, Admetus stays by her side the whole entire time. Also, since i see her as the mate of Gus, it makes the idea of Admetus being their son pretty realistic.
Grizabella
Just about half of the CATS fandom thinks that in the past, Old Deuteronomy and Grizabella were mates. If so, then there is a large chance that she could be Admetus mother. He is a very msyerious tom and little is known about him. Plus, he has similar coloring to Grizabella's and his fur is similar to Old Deuteronomy's as well.
This might also be the reason he glares at her with so much haterd when she shows up. He also hisses at her later on in the show when she returns.
Jennyanydots
Jennyanydots has proven herself to be a wonderful motherly figure so there could be a chance that Admetus is one of her sons.
Now, I know what you're thinking. Admetus is pretty old and he is certainly no kitten but he could still he her son. Just because he's not a kitten doesn't really mean anything.
https://www.angelfire.com/crazy/quidam_1/strongsilent/main.html
