A theory on incoherently coupled soliton pairs for photorefractive screening solitons is developed that gives rise to incoherently coupled steady-state soliton pairs and multicomponent spatial solitons in biased photorefractive-photovoltaic materials, which result from both the bulk photovoltaic effect and the spatially nonuniform screening of the external bias field. When the bulk photovoltaic effect is neglectable, these soliton pairs are the previously studied soliton pairs for screening solitons, these multicomponent spatial solitons predict incoherently coupled multicomponent spatial solitons for screening solitons, and their space-charge field is the space-charge field of screening solitons. When the external field is absent, these soliton pairs and multicomponent spatial solitons predict incoherently coupled soliton pairs and multicomponent spatial solitons for photovoltaic solitons, and their space-charge field is the space-charge field of photovoltaic solitons. The stability of these soliton pairs and multicomponent spatial solitons is also discussed using the modulation instability theory.