Most IATA member airlines have an interline agreement with each other, which allows transfer of baggage. I don't know if PAL does but it is likely to (generally LCCs do not interline, for example Southwest in the US and Ryanair in Europe). Lately some airlines have stopped interlining for separate tickets (they do interline for the same ticket); BA does this, for non-Oneworld separate tickets, for example.

The other consideration is customs clearance. Some countries require baggage to be collected and presented to customs by the passenger at the first port of entry (MNL in your example); other countries do not require this. You can check with Phillipine customs whether this is the case.