If you're using anti-APC microbeads for enriching your cell population of interest while labelling with FITC and PE is for purpose of subsequent cell sorting, why don't you label your cells with APC-conjugated antibody alone first and magnetically enrich with anti-APC microbeads followed by labelling with FITC and PE? That will avoid any cross-reactivity issue you're worried about.

I must congratulate you on thinking about this potential cross-ractivity between APC and PE. The remedy is as suggested in the previous answer. Do this in two steps so there is no possibility of cross-reaction between APC and PE.

If you are doing FACS why not sort the APC+ cells if you don't need too many cells. This way you can nicely distinguish APC only versus any double or tiple positive cells.

In my experience, at least the antibodies used from Miltenyi Biotec do not crossreact. No problem to sort APC in the presence of PE.