We indicate how one can extend any dynamical system (namely, any system of nonlinearly coupled autonomous ordinary differential equations) so that the extended dynamical system thereby obtained is either isochronous or asymptotically isochronous or multi-periodic, namely its generic solutions are either completely periodic with a fixed period or tend asymptotically, in the remote future, to such completely periodic functions or are multi-periodic (or become multi-periodic only asymptotically, in the remote future).In all cases the scale of the periodicity can be arbitrarily assigned.Moreover, the solutions of the extended systems are generally well approximated by those of the original, unmodified, systems, up to a constant rescaling of the independent variable (time), as long as their evolution is considered over time intervals short with respect to the (arbitrarily assigned) periodicities characterizing the extended systems.Several examples are displayed.In some cases the general solution of these dynamical systems is also exhibited; in others, this is impossible inasmuch as the models being manufactured are extensions of dynamical systems displaying chaotic evolutions, such as, for instance, the well-known Lorenz model of 3 nonlinearly coupled ODEs.