Digital programmable metasurfaces provide a very powerful and versatile platform for implementing spatio-temporal modulation schemes that are of great interest within the emerging framework of space-time metastructures. In particular, space-time coding digital metasurfaces have been successfully applied to advanced wavefront manipulations in both the spatial and spectral domains. However, conventional space-time coding schemes do not allow the joint syntheses of the transmission/scattering angular responses at multiple frequencies, which are potentially useful in a variety of applications of practical interest. Here, a strategy is put forward to lift this limitation, thereby enabling joint multi-frequency beam shaping and steering, i.e., the independent and simultaneous syntheses of prescribed scattering patterns at given harmonic frequencies. The proposed approach relies on a more sophisticated space-time coding, with suitably designed, temporally intertwined coding sub-sequences, which effectively disentangles the joint multi-frequency syntheses. The power and versatility of the approach are illustrated via a series of representative application examples, including multi-beam, diffuse-scattering, and orbital-angular-momentum patterns. Theoretical predictions are experimentally validated by means of microwave measurements. The outcomes of this study hold promising potentials for applications to future imaging, information and mobile-communication systems.