This paper proposes a new bi-level multidisciplinary design optimization architecture (or MDO formulation) with variants and proves their convergence properties. MDO architectures are reformulations of an original MDO problem into one or combined optimization problems. Distributed architectures define several optimization problems, and can be exploited in industrial contexts to map the separation of responsibilities, models, and computational resources in the design of sub-systems. Also, they allow to use only some disciplinary blocks of the overall MDO problem Jacobian, and do not require the complete coupled adjoint, which is rarely available in an industrial context. These advantages come at the price of weaker convergence properties compared to monolithic architectures. The IRT bi-level architecture, which falls within this category, is derived from the MDF architecture and is highly reliant on a block decomposition of the lower optimization problem, in which blocks are optimized in parallel. In order to enhance its convergence capability, a novel bi-level architecture is proposed (BL-BCD-MDF), which solves the lower optimization problem using the well-known Block Coordinate Descent (BCD) algorithm. The primary findings of this study are twofold. First, under appropriate hypotheses, the solutions of the reformulated optimization problems are identical to those of the MDF optimization problem, and the BL-BCD-MDF architecture is locally convergent. Variants are proposed to enhance flexibility in assumptions and the decomposition. To the authors' knowledge, this is the first convergence proof of a distributed MDF bi-level MDO architecture in the MDO literature. The architectures are benchmarked on standard MDO problems (Sellar and Sobieski's SSBJ). Improved functions continuity and robustness than the IRT bi-level is demonstrated, as well as a superior scalability with respect to disciplinary design variables than MDF when the full Jacobian is not available.