Quadratic Hawkes (QHawkes) processes have proved to be very effective at reproducing the statistics of price changes, capturing many of the stylised facts of financial markets. Motivated by the empirical cross Zumbach effect and by the strong occurrence of endogenous co-jumps (simultaneous price jumps of several assets), we can extend QHawkes to a multivariate framework (MQHawkes), which now considers several financial assets and their interactions. Assuming that quadratic kernels write as the sum of a time-diagonal component (Hawkes component) and a rank one (trend) contribution, endogeneity ratios and the resulting stationarity conditions can be studied. Developing the Yule-Walker equations for the multivariate process, empirical intraday data can then be used to calibrate the model.