  Phase transitions in isotropic quantum antiferromagnets are associated with
the condensation of bosonic triplet excitations. In three dimensional quantum
antiferromagnets, such as TlCuCl$_3$, condensation can be either pressure or
magnetic field induced. The corresponding magnetic order obeys universal
scaling with thermal critical exponent $\phi$. Employing a relativistic quantum
field theory, the present work predicts the emergence of multiple (three)
universalities under combined pressure and field tuning. Changes of
universality are signalled by changes of the critical exponent $\phi$.
Explicitly, we predict the existence of two new exponents $\phi=1$ and $1/2$ as
well as recovering the known exponent $\phi=3/2$. We also predict logarithmic
corrections to the power law scaling.
