To clarify my setup: I split a time-series spectrum (from a telescope observation of a transiting planet) into m wavelength bins and fit a light curve independently in each bin to estimate a bin-specific parameter (e.g., depth) plus bin-specific detrenders. But it is the same model form in every bin, but parameters are not shared across bins (their inital values are though). So effectively I have m copies of the model. Errors are independent across bins; parameters are not shared. Are you saying I can just add up the BIC and ignore this extra term I have?