How to download app updates from different account than original app purcha

I have a collection of apps on my iPhone that I bought through my original iTunes account, then later I signed up for a second account (because I was confused and I didn't know what I was doing) so my more recent apps were bought through that second account. I really would like to close the older account because I have no use for two separate accounts.

But here's the problem: when I update an app, iTunes remembers what account I originally bought it under and asks me to sign in to that account. So if I close the older account I will no longer be able to update any apps that I purchased under that account. Is there a way I can fix it so that I can close the old account but still be able to update those other apps?