Do you know of any flight packages that would take me to Taiwan, South Korea and the Philippines, enabling me to fly to various cities in these three countries?

I know that Cathay Pacific and Malaysian AIr both have airpasses. I would check with the airlines for these countries - Korean Air, Asiana, EVA, Philippine Air - to see if any of them have airpasses. The problem with almost all of the airpasses is that they require to you fly back through the hub every time you change location.

I have never heard of any flight packages that include unlimited multi country destinations as well as domestic flights in each of the country you have mentioned. As Kathie have said the known air passes will require that you fly back to each country's hub before going to a new country.

http://www.staralliance.com/en/fares.../asia-airpass/

mrwunfl as far as I know the Star Alliance air pass does not cover domestic Philippines and Taiwan air travel which is what the OP require.

The *A pass might be an option for all of the international travel without returning to one airlines' hub. The planning map shows Busan as an option as well as Seoul. Manila, Cebu, and another Phillpines city. Not necessary to fly within Taiwan, I think.

Would have to buy a ticket for domestic Phillipines travel unless Phillipines Airlines has its own domestic air pass.

An airline pass for a single airline might work, with Seoul or Taipei as the hub. Maybe Korean, Asiana, EVA, China Airlines.