  Many theories beyond the Standard Model of particle physics predict the
existence of axionlike particles (ALPs) that mix with photons in the presence
of a magnetic field. Searching for the effects of ALP-photon mixing in
gamma-ray observations of blazars has provided some of the strongest
constraints on ALP parameter space so far. Previously, only individual sources
have been analysed. We perform a combined analysis on $\textit{Fermi}$ Large
Area Telescope data of three bright, flaring flat-spectrum radio quasars, with
the blazar jets themselves as the dominant mixing region. For the first time,
we include a full treatment of photon-photon dispersion within the jet, and
account for the uncertainty in our B-field model by leaving the field strength
free in the fitting. Overall, we find no evidence for ALPs, but are able to
exclude the ALP parameters $m_a\lesssim200$ neV and $g_{a\gamma}\gtrsim 5
\times 10^{-12}$ GeV$^{-1}$ with 95\% confidence.
