"what this should do?". Processlist would then have one more column ('PRIORITY*). And the value of that column is the priority with what the OS executes this paricular thread (forever in the lifetime of the thread or for the time of current query only - could be one more parameter). But my system knowledge is not deep enough to decide if the idea is feasible wtit reasonable effort. I actually don't know if priorities are only available for processes and not threads in various OS'es. If the control should be implemented inside the server without calling OS routines, I realize it is a huge project.
Also my proposed syntax should more be seen as 'pseudo code' than an actual implementation. But SET PRIORITY [FOR THIS] could make sense if it could also be executed from clients/scripts running with sufficient privileges. You may want to SET PRIORITY *low* ("don't let this thread have any impact on other threads") - but also maybe sometimes to set it *high* in some cases ("this is more important than anything else and it does not matter if other threads suffer").
If you can afford a server instance (virtual or not) per customer there are many posibilities. But that is not Marian's environment I think. If it was, she would not have found the solution inside MySQL. I understand that this is about management of traditional 'shared hosting', where users/customers that are completely unrelated and have no knowledge of each others share access to a MySQL server - only managed by different user accounts and their privileges.
-- Peter