Yup it seems quite a few do.
Paph chamberlainianum has a new flower & growing a new planlet.
Phrag SA is flowering , growing 3 new leads.
Phal Anthur"Delhi) growing a spike , new roots & a new leaf.
Continious or sequential flowerers normally will be growing new leads as the
mature 1 flowers.
Phsychopsis papilio flowers for years so it must do all the activities @ the same time as flowering.