This paper introduces convex soft geometries. The import of this model is that it extends a successful field of research, namely convex geometries, to account for alternatives characterized by a multiplicity of attributes. Related concepts include soft convex hulls and a notion of extreme elements. Some fundamental results are proven. Among them, we guarantee that an anti-exchange property holds true. Importantly, the existence of extreme elements is guaranteed, hence proving their suitability for applied studies. Both results are natural (but non-trivial) extensions of comparable outputs for convex geometries. We present a detailed research program that might stimulate future investigations on this new research area.