You can certainly pay someone else's attorney's fees if you so choose; however, this does not give you any rights regarding the relationship between that attorney and his or her client. In other words, an attorney shares attorney-client privilege with his or her client regardless of who is paying the fee. If you have adverse interests in the case, then there might be a conflict of interest in you paying someone else's bills.
The information provided herein is general information only and not legal advice. The information provided herein does not create an attorney client relationship and is not a substitute for having a consultation with an attorney. It is important to have a consultation with an attorney as the information provided in this forum is limited and cannot possibly cover all potential issues in a given situation