The azimuthal anisotropy Fourier coefficients (v(n)) in 8.16 TeV p + Pb data are extracted via long-range two-particle correlations as a function of the 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 p + Pb collisions. The v(2) and v(4) coefficients are found to be positively correlated in all collision systems. For high-multiplicity p + Pb 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 p + Pb and PbPb collisions in the measured multiplicity range.