While heterogeneous adoptability of agents and compatibility of multiple contagious entities are omnipresent in social contagion, these factors are overlooked in traditional models of contagion processes. Here, we study contagion processes in two directions: i) unifying simple and complex contagion reflecting heterogeneous adoptability and ii) considering competition and compatibility among multiple transmittable entities. For a generalized contagion model unifying simple and complex contagion processes, we find a rich variety of phase transitions such as continuous and discontinuous phase transitions, criticality, tricriticality, and double transitions. We also examine the role of dual users who possess multiple contagious technologies simultaneously, and find that the compatibility induced by the dual user facilitates spread of innovation and extinction of preexisting technology.