*multi-party system intensifies*

And VP has separate elections from President.

And also, the Philippines has a President of the Senate, while in the US the Vice President is the head of the Senate. Originally, in the US Constitution, the VP was the presidential candidate with the second most votes in the election.
But then the Twelfth Amendment changed it so that the President chooses a running mate.
Honestly I like the old system better

Yeah. Because sometimes you don't like the VP but like the President, or like the VP but not the President. Leni Robredo's running for President and I really support her but I don't really like her VP, Kiko Pangilinan. The old system allows people to also choose who they want as VP even if they don't like their running mate.

How many parties are there?

41 national parties, with about 12-14 having seats in Congress