protection circuit

OK, so I bought a cheap 5 volt power bank designed for charging phones. Inside it was a 3.7 volt, 2200 mah lithium ion battery and a protection circuit that boosts the output to 5 volts. Can I hook up a different battery to the circuit? I have some 3.7 volt, 3200mah lipo batteries that I'd like...

So I was looking at my battery situation last night and I had a question: Each pack is 7.4 V. One of the packs protection circuit seems to be broken. I checked the individual batteries with my multimeter and I get 7.4V but when I check the voltage from the protection circuit I don't get...