yes, this can easily be done but will require a custom report. Firstly, if you want to group by Saveset, you will need to provide the saveset field to the report, so copy and mofify the Report Card report and on the Properties of the "Num Save Sets" (or "Nuim Jobs" depending on what terminology you are using), on the Group By tab, tick/check the "saveset" field as well ie. group by client, status and saveset.
Then in the Report Appearance Toolbar , use the Field Mapping icon (the yellow cylinder) to multi-select BOTH the client and the saveset field and that should do the trick.
If you want to use the drill-downs as well, you will also need to create custom versions of the Backup Save Set Summary and those it calls - and the change would be to pass the saveset name through to each drill down report too.
I have tested this in our demo environment