It can be very difficult to find a bank that has accounts that can be accessed in the Philippines. Most banks run their country offices as a separate entity. However, there are a few allow you do banking between the Philippines and US (international) offices.
HSBC allows you to open international Premier bank accounts where you can make deposits in the US (or any location), and the funds are available for withdrawal in any International HSBC branch, including the Philippines.
Its important to note that b/c of Philippine laws, the limit that can be withdrawn without higher approval is $2k within a 48-hour period. Any more than that, and there are further identification measures which occur at the Philippine branch. You must provide identifications and get approval from the specific branch that you visit in PH.
Withdrawal Limit: $2k (in 48 hr period). Anything higher requires identification and approval by the PH branch you visit. Over $2k is not guaranteed, and is subject to approval of that local bank's branch manager. They refer to these international withdrawals as "Emergency Encashments"
Although BoA does not offer a true international account, it allows one of the highest ATM withdrawal amounts of any US bank.
The amount you can withdraw depends on your Account type, but the general DAILY LIMIT is: