  We obtain a general Marcinkiewicz-type multiplier theorem for mixed systems
of strongly commuting operators $L=(L_1,...,L_d);$ where some of the operators
in $L$ have only a holomorphic functional calculus, while others have
additionally a Marcinkiewicz-type functional calculus. Moreover, we prove that
specific Laplace transform type multipliers of the pair $(\mathcal{L},A)$ are
of certain weak type $(1,1).$ Here $\mathcal{L}$ is the Ornstein-Uhlenbeck
operator while $A$ is a non-negative operator having Gaussian bounds for its
heat kernel. Our results include the Riesz transforms $A(\mathcal{L}+A)^{-1}$
and $\mathcal{L}(\mathcal{L}+A)^{-1}.$
