  The composition of a jet is still an unsolved problem in gamma-ray bursts
(GRBs). Several previous studies have suggested that the prompt emission
spectrum of GRBs is likely to consist of a few components that may arise from
different jet compositions. Here we present a systematic analysis to search for
the GRBs that seem to show the transition from a fireball to the
Poynting-flux-dominated outflow between well-separated pulses within a single
burst, like the GRB 160626B, using the Gamma-ray Burst Monitor data of the
\emph{Fermi} satellite. We obtain 43 GRBs with clear multiple pulses and find
that 9/43 (21\%) bursts may exhibit such a transition based on the
time-integrated spectral analysis. We then select a further four bursts with
the data of adequate quality to perform a detailed time-resolved spectral
analysis, and we find that in three bursts the thermal-like pulse is a
precursor. Furthermore, based on the time-resolved spectra, we constrain the
outflow properties for those thermal pulses and find them consistent with the
typical properties of the photosphere emission. Also, the later pulses with the
softer low-energy spectral index are compatible with the optically thin
synchrotron emission model. Our analysis indicates that a good fraction of the
multipulse {\it Fermi} bursts may obtain the transition from fireball to the
Poynting-flux-dominated outflow.
