In our prior work, we proposed the IQ-ASyMTRe architecture as a general method to combine coalition formation and execution for tightly-coupled multirobot tasks. IQ-ASyMTRe extends the ASyMTRe architecture by introducing several new mechanisms to provide more flexibility for coalition formation as well as to facilitate coalition execution. On the other hand, these mechanisms also change the process of reasoning about solutions and further increase the complexity of the solution space. In this paper, we provide improvements for utilizing the IQ-ASyMTRe architecture based on reasoning about the solution space. We introduce a method in which the exponential growth of the number of potential solutions to be searched can be avoided; instead, the search space is only of linear size for certain tasks. Unnecessary potential solutions are removed to further increase online efficiency. Moreover, the relationships between the created solution space and the complete solution space are studied, and are utilized to provide more coverage of the complete solution space for arbitrary tasks. Although these improvements are discussed with respect to IQ-ASyMTRe, they are also applicable to architectures that approach the generality that IQ-ASyMTRe achieves. Robot simulation and experimental results are provided to demonstrate that the generation and searching of the solution space can be done online (which was impractical previously even for tasks with relatively modest complexities) for certain tasks, and to illustrate how our approach impacts the solution space.