We generalize the concept of an incomplete double group divisible design and describe some recursive constructions for such a generalized new design. As a consequence, we obtain a general recursive construction for group divisible designs, which unifies many important recursive constructions for various types of combinatorial designs. We also introduce the concept of a double frame. After providing a preliminary result on the number of partial resolution classes, we describe a general construction for double frames. This construction method can unify many known recursive constructions for frames.