You've got yourself an interesting opportunity here.
My experience on supermarkets is well into the hundreds, with car park cleaning a large part but these would all be classed as ad hoc/one off cleans with only pressure washing as the option.
There are car parks out there that are never litter picked - the wind gets rid of the rubbish & then there are those that have a quick litter pick as the guy changes the store front litter bin bags - never seen this motorised service offered.
If I was offered multiple sites I would probably give him a price per 5, 10, 15 etc, taking into account travel time between them, forming the round.
The supermarkets have tight pockets.
I knew of a gutter cleaning budget that was approved - into the hundreds of thousands but was never used, by the time I got to hear about it the contact went off on maternity leave & it never went anywhere.
Only six weeks ago I chatted to a guy on a store car park who had multiple sites for gritting, similar principles, he's putting it down your taking it off, he was less than half an hour, then I'm onto the next store & he's there again, think he'd got 5 or 6.
Are you towing it round on a trailer?
I'd be happy to work with you or both of you to make it happen.