Weproposetheoreticallyandverifyexperimentallyamethodofcombiningaq-plateandaspiralphaseplatetogeneratearbitraryvectorvortexbeamsonahybrid-orderPoincarésphere.Wedemonstratethatavectorvortexbeamcanbedecomposedintoavectorbeamandavortex,wherebythegenerationcanberealizedbysequentiallyusingaq-plateandaspiralphaseplate.Thegeneratedvectorbeam,vortex,andvectorvortexbeamareverifiedandshowgoodagreementwiththeprediction.Anotheradvantagethatshouldbepointedoutisthatthespiralphaseplateandq-platearebothfabricatedonsilicasubstrates,suggestingthepotentialpossibilitytointegratethetwostructuresonasingleplate.Basedonacompactmethodoftransmissive-typetransformation,ourschememayhavepotentialapplicationsinfutureintegratedopticaldevices.