We use a large database of known molecular semiconductors to define a plausible physical limit to the charge carrier mobility achievable within this materials class, and a clear path toward this limit. From a detailed study of the desirable properties in a large dataset, it is possible to establish whether such properties can be optimized independently and what would be a reasonably achievable optimum for each of them, regardless of the transport mechanism considered. We compute all relevant parameters from a set of almost five thousand known molecular semiconductors, finding that the best known materials are not ideal with respect to all properties. These parameters in decreasing order of importance are realized to be the molecular area, the non-local electron-phonon coupling, the two-dimensional nature of transport, the local electron-phonon coupling and the highest transfer integral. We also find that the key properties related to the charge transport are either uncorrelated or 'constructively' correlated (i.e. they improve together) concluding that a ten-fold increase in mobility is within reach in a statistical sense, on the basis of the available data. We demonstrate that high throughput screenings, when coupled with physical models of transport produce not only specific target materials, as it is done also here, but a more general physical understanding of the materials space and the opportunities of further development.