How do you approach treating patients who develop psoriasis while on Dupixent?  

Stop the Dupixent. These patients likely had a non-Th2 driven type of dermatitis e.g. Malassezia yeast hypersensitivity, which is Th17 driven, or stasis dermatitis with autoeczematization, or eczematous drug reaction. Revisit the Diagnostic Checklist for Generalized Dermatitis.

If the psoriasis is limited in extent, topicals may be entirely reasonable and feasible. Ones that control both psoriasis and atopic dermatitis might be the most sensible. If the psoriasis were to extensive for topicals alone, phototherapy or systemic treatment may be perfectly reasonable.