We've adopted babies, domestically....three times. (A total of five times if you count the international babies before them.)
If you're wanting, you can do both! If you're dealing with an agency or attorney or facilitator that requires substantial $$ up front or....'at match' as they love to say, that might limit you; but honestly, everyone SHOULD be willing to allow you to deal with several entities at one time.
If you're not sure, feel free to pm me. But I know in our pursuits, we've always worked with more than one agency and attorney at one time.
Best of luck to you...
Sincerely,
Linny