This article describes the lattice of varieties generated by those of flocks and near heaps. Flocks and heaps are two ways of presenting groups by a ternary operation rather than a binary one. Their varieties joined with that of ternary semilattices create the varieties of near flocks and near heaps. This is done by finding normal forms for words that make up free algebras. Simple sets of identities define these varieties. Identities in general are decidable. Each near flock is a Plonka sum of flocks, and each near heap is a Plonka sum of heaps. An algorithm translates any binary group identity to one in a ternary operation satisfied by near heaps.