  The Malgrange-Galois groupoid of Painlev\'e IV equations is known to be, for
very general values of parameters, the pseudogroup of transformations of the
phase space preserving a volume form, a time form and the equation. Here we
compute the Malgrange-Galois groupoid of Painlev\'e VI family including all
parameters as new dependent variables. We conclude it is the pseoudogroup of
transformations preserving parameter values, the differential of the
independent variable, a volume form in the dependent variables and the
equation. This implies that a solution of Painlev\'e VI depending analytically
on parameters does not satisfy any new partial differential equation (including
derivatives w. r. t. parameters) which is not derived from Painlev\'e VI.
