Dear Miguel,
I think spOcc/spAbu does not (yet ?) have any models for species co-occurrence of the kind that you mention, e.g., like the models developed by Chris Rota and colleagues around 2016. For this, you would have to go to unmarked or code them up in JAGS/NIMBLE/Stan.
However, one might still learn something about co-occurrence patterns from a model fit in spOccupancy, based on posterior draws of z, i.e. the presence and absence of each species. You can get z for each site in your analysis in R, by calling the function rbinom with sample size equal to 1 (for a Bernoulli) and with prob = the predicted occupancy probability (psi) obtained from a call to spOccupancy:: predict. Doing this once for each posterior draw of psi at every pixel gives you the posterior distribution of z for every pixel. Then, you can summarize these for two or also more species in a tabulation that gives you the number of pixels where only one species occurs, only the other, both, or none. This will be more descriptive than what the Rota et al-type of models can teach you, but inspecting such patterns may still give you a lot of insight into community structure.
Best regards --- Marc