The evidence for short prophylaxis treatments is low. It's much better to have the tick tested, then you'll know what it was carrying. Doxy doesn't work against all tick-borne diseases.
Guidelines do not call for treating lyme plus coinfections prophylactically.
You're not going to get a Dr. prescribing Mepron and then Rifampin for a tick bite.
Note: Malaria prophylactic for travel is doxycycline...so perhaps it works for babesia as well
...and uncomplicated bartonella - I see doxy is listed as treatment.