The azimuthal anisotropy Fourier coefficients ($v_n$) in 8.16 TeV pPb data are extracted via long-range two-particle correlations as a function of event multiplicity and compared to corresponding results in pp and PbPb collisions. Using a four-particle cumulant technique, $v_n$ correlations are measured for the first time in pp and pPb collisions. The $v_2$ and $v_4$ coefficients are found to be positively correlated in all collision systems. For high multiplicity pPb collisions an anticorrelation of $v_2$ and $v_3$ is observed, with a similar correlation strength as in PbPb data at the same multiplicity. The new correlation results strengthen the case for a common origin of the collectivity seen in pPb and PbPb collisions in the measured multiplicity range.