Can you be reinfected if you and your partner both have hpv?

Yes, you can: Hpv has numerus strains; some cause cancer. A person can get more than one type of hpv. Get regular pap smears form your doctor.

Not really: This does not ping pong back and forth like a strep throat might. Once you and your partner share the same strain of HPV, it would clear the primary infection over time ( by developing antibodies) but could stay in your system forever & reactivate. You could pass it to an uninfected person but not to someone who has had the strain.

Possibility mayexist: There are several dozens of benign HPV's and dozens of high-risk-oncogenic HPV's. If you and or your partner were to acquire a new strain or a new subtype of the human papilloma virus against which neither of you have immunity (the right antibodies) there is a theoretical and perhaps real possibility that you could infect (seemingly"reinfect") each other with this new HPV.