First of all, if you are interested in multi-mappers quantification, you do not want to use htseq-count, you want to use RSEM, Salmon or kallisto. Although your current post doesn't say you are using htseq-count, your previous post does.
According to the post Multimapping Reads and Pseudogenes, STAR has fairly stringent parameters and one mismatch between the best match and second-best match is enough to exclude the second-best mapping position, so in general, I would expect for most pseudogenes it is not necessary to alter
--outFilterMultimapNmax, unless the duplication is fairly recent and / or gene and pseudogene are identical over a large stretch (longer than your sequencing read length).
Based on your past thread, it seems you are interested in a particular gene / pseudogene pair, as opposed to interested in transcription expression of all pseudogenes in the genome. If that is the case, you have to find out how similar PER3 and PER4 (and potentially PER1 and PER2) are. You can also test different
--outFilterMultimapNmax settings and visualize the regions of interest with IGV to see how mapping there is affected.