You can have one credit card account and two separate cards linked to two different rewards network accounts.

Example:
I have a Hilton Honors Amex, this gives 5 HH points per USD spent at restaurants. I add this account to my AA rewards network account. I earn 5 HH and 10 AA per USD spent.

I now request an additional signer be added to my HH AMEX and take out the card in my own name. Amex will not do any credit check whatsoever. The card will arrive with a different account number and then I add the Card number to my UA rewards network account.

All HH points now post to the same account. All charges now post to the same Amex account. I now carry 2 Credit cards, one marked UA and the other marked AA.