This can be done using a Publication with Dynamic Recipients.
You would need to create a second report that would produce a list of all values in your Client dimension. This report would then serve as the source of the Dynamic Recipients in the Publication. In the base report, you would remove the prompt on Client but make sure that Client is included in the report results. Then in the Publication, you would set Personalization such that a filter is automatically applied to the Client dimension based on the values from the second report.