  We propose a minimal generalization of the celebrated Markov-Chain Monte
Carlo algorithm which allows for an arbitrary number of configurations to be
visited at every Monte Carlo step. This is advantageous when a parallel
computing machine is available, or when many biased configurations can be
evaluated at little additional computational cost. As an example of the former
case, we report a significant reduction of the thermalization time for the
paradigmatic Sherrington-Kirkpatrick spin-glass model. For the latter case, we
show that, by leveraging on the exponential number of biased configurations
automatically computed by Diagrammatic Monte Carlo, we can speed up
computations in the Fermi-Hubbard model by two orders of magnitude.
