  We consider stochastic mSQG (modified Surface Quasi-Geostrophic) equations
with multiplicative transport noise of Kraichnan type, and $L^p$-initial
conditions. Inspired by the recent work of Coghi and Maurelli
[arXiv:2308.03216], we show weak existence and pathwise uniqueness of solutions
to the equations for suitable choices of parameters in the nonlinearity, the
noise and the integrability of initial data.
