An existing extension of the Cooperative Task Space is reformulated in the dual quaternion domain to form the Extended Cooperative Dual Task Space (ECDTS).This representation allows for the description of both uncoordinated and coordinated cooperative manipulation tasks into a unified formulation free of representational singularities. Additionally, a general framework is proposed to describe cooperative manipulation tasks considering the required manipulation mode in the ECDTS, the desired control objective, and additional task constraints. Vector Field Inequalities (VFIs) and geometric primitives such as Plücker lines and planes are used to define such constraints. Simulations of a task from each manipulation mode are carried out and show the generality of the proposed framework and applicability of the ECDTS formulation.