This is a hot topic in main group chemistry, and has been used to explain stable CO complexes with main group elements.
Here is a very nice open-access article by Sergeieva et al. where they look at the pi-back donation with some state-of-the-art computational chemistry.
Here's a graphical demonstration of the Si←CO σ-donation and Si→CO π-back donation.
Figure 2 Plot of deformation densities Δρ1–3 (isovalue=0.003) of the pairwise orbital interaction and shape of the most important occupied and vacant orbitals (isovalue=0.03) in silylene−carbonyl complex 1 with the orbital interaction energies ΔEorb (in kcal/mol) and their eigenvalues ν (in e). For the deformation densities, the direction of the charge flow is red→blue. The eigenvalues ν indicate the amount of donated (negative numbers) and accepted charge (positive numbers). The occupied orbitals are shown in yellow and blue for the different phases, while the unoccupied orbitals are in cyan and orange. Reproduced with permission according to CC BY 4.0 license.
The references contained therein detail the long history of Si--CO backbonding in particular.
There is nothing to stop back-donation to non-metal centers, but it is much rarer with main group elements.
This is likely just because it happens to be that the overlap is more likely to occur with metals due to, e.g., ionic radius, d-orbital shape, etc..