Generally, no—because Palestine does not recognize dual citizenship.
The Palestinian Authority (PA) considers Palestinian nationality exclusive. Acquiring another citizenship automatically terminates Palestinian nationality (Palestinian Citizenship Order 1925, amended; PA practice). No formal dual citizenship framework exists.
The Philippines allows dual citizenship under RA 9225 (Citizenship Retention and Re-acquisition Act, 2003)—but only for:
A Palestinian national (not a natural-born Filipino) cannot use RA 9225. If they naturalize Filipino, they lose Palestinian status. If they're already Filipino (by birth/descent), they're not "a Palestinian national acquiring Filipino nationality"—they're a dual citizen by birth, but Palestine may not recognize it.