This is the third in a series of papers devoted to studying intermediate- mass molecular outflows and their powering sources in detail and with high -angular resolution. This paper studies the intermediate-mass YSO IRAS 20050+2720 and its molecular outflow and puts the results of this and the previous studied sources in the context of intermediate-mass star formation. We carried out VLA observations of the 7mm continuum emission and OVRO observations of the 2.7mm continuum emission, CO (1-0), C18O (1-0) and HC3N (12-11) to map the core towards IRAS 20050+2720. The high-angular resolution of the observations allowed us to derive the properties of the dust emission, the molecular outflow, and the dense protostellar envelope. By adding this source to the sample of intermediate-mass protostars with outflows, we compared their properties and evolution with those of lower mass counterparts. The 2.7mm continuum emission has been resolved into three sources, labeled OVRO 1, OVRO 2, and OVRO 3. Two of them, OVRO 1 and OVRO 2, have also been detected at 7mm. OVRO 3, which is located close to the C18O emission peak, could be associated with IRAs 20050+2720. The mass of the sources, estimated from the dust continuum emission, is 6.5M_{sun}_ for OVRO 1, 1.8M_{sun}_ for OVRO 2, and 1.3M_{sun}_ for OVRO 3. The CO (1-0) emission traces two bipolar outflows within the OVRO field of view, a roughly east-west bipolar outflow, labeled A, driven by the intermediate-mass source OVRO 1, and a northeast-southwest bipolar outflow, labeled B, probably powered by a YSO engulfed in the circumstellar envelope surrounding OVRO 1. The multiplicity of sources observed towards IRAS 20050+2720 appears to be typical of intermediate-mass protostars, which form in dense clustered environments. In some cases, as for example IRAS 20050+2720, intermediate- mass protostars would start forming after a first generation of low-mass stars has completed their main accretion phase. The properties of intermediate-mass protostars and their outflows are not significantly different from those of low-mass stars. Although intermediate-mass outflows are intrinsically more energetic than those driven by low-mass YSOs, they do not show intrinsically more complex morphologies when observed at high angular resolution. Known intermediate-mass protostars do not form a homogeneous group. Some objects are likely in an earlier evolutionary stage as suggested by the infrared emission and the outflow properties.