In a wait-free model any number of processes may crash. A process runs solo when it computes its local output without receiving any communication from other processes, either because they crashed or they are too slow. While in wait-free shared-memory models at most one process may run solo in an execution, any number of processes may have to run solo in an asynchronous wait-free message-passing model. This paper is on the computability power of models in which several processes may concurrently run solo. It first introduces a family of round-based wait-free models, called the d-solo models, 1 ≤ d ≤ n, where up to d processes may run solo. The paper gives then a characterization of the colorless tasks that can be solved in each d-solo model. The paper introduces the (d, epsilon)-solo approximate agreement problem, which generalizes epsilon-approximate agreement. It proves that (d, epsilon)-solo approximate agreement can be solved in the d-solo model, but it cannot be solved in the (d + 1)-solo model. The paper also studies the relation linking d-set agreement and (d, epsilon)-solo approximate agreement in asynchronous wait-free message-passing systems. These results establish for the first time a hierarchy of wait-free models weaker than the basic read/write model, that are nevertheless still strong enough to solve many tasks. The new failure model, based on taking into account solo executions, has message passing as well as shared-memory instantiations.