  The Ott--Antonsen ansatz is a powerful tool to extract the behaviors of
coupled phase oscillators, but it imposes a strong restriction on the initial
condition. Herein, a systematic extension of the Ott--Antonsen ansatz is
proposed to relax the restriction, enabling the systematic approximation of the
behavior of a globally coupled phase oscillator system with an arbitrary
initial condition. The proposed method is validated on the Kuramoto--Sakaguchi
model of identical phase oscillators. The method yields cluster and
chimera-like solutions that are not obtained by the conventional ansatz.
