I had three credit card accounts with one credit card company...they kept one open, closed the other two. Then said you have one account with the credit line of all three in one. THEN HE SAID "THE CREDIT LINE IS TOO LOW...IN ABOUT ONE MINUTE IT WILL BE $5,000 MORE"!!!
I love managing credit. I have 4 accounts with Chase, they don't charge me a fee. I have a Cap one account and they charge me no fee. I just closed a Cap 1 business account because their limit of $1500 did not warrant a $59 annual fee.
Combining accounts is a matter of convenience for both the issuer and the holder. In most cases, there are no account fees involved. I would think this could be done.
Capital one will combine accounts which have been opened for 6 months. However, they do not like to do this because like you said, they lose the annual fees. So when trying this you may have to insist. Hope this helps.