A major goal of synthetic biology is to reprogram living organisms to solve pressing challenges in manufacturing, environmental remediation, or healthcare. While many types of genetic logic gates have been engineered, their scalability remains limited. Previous work demonstrated that Distributed Multicellular Computation (DMC) enables the implementation of complex logic within cellular consortia. However, current DMC systems require spatial separation of cellular subpopulation to be scalable to N-inputs, and need cell-cell communication channels to operate. Here we present scalable composition frameworks for the systematic design of multicellular consortia performing recombinase-based Boolean or history-dependent logic, and integrating an arbitrary number of inputs. The theoretical designs for both Boolean and history-dependent logic are based on reduced sets of computational modules implemented into specific cellular subpopulations which can then be combined in various manners to implement all logic functions. Our systems mark a departure from previous DMC architectures as they do not require either cell-cell communication nor spatial separation, greatly facilitating their implementation and making them fully autonomous. Due to their scalability and composability, we anticipate that the design strategies presented here will help researchers and engineers to reprogram cellular behavior for various applications in a streamlined manner. We provide an online tool for automated design of DNA architectures allowing the implementation of multicellular N-inputs logic functions at:http://synbio.cbs.cnrs.fr/calin.