Some of the phone shops I do are one per client per day, but if you are working with more than one client it is one each per day. As Mert mentioned, the MSP company you are working with may have limits on total shops for them, but they cannot control what you do for other companies. Some shoppers set up routes of shops that may have 20 or more shops per day.
How many shops I will attempt in a day depends to a great extent on the report. There are shops that I can handle the reports for 5 in an hour, there are shops where each report takes an hour or more. There are shops where I spend no more than 5-10 minutes at the store, there are shops where I need to be in the store often for more than an hour. You need to perform the shops to find out how long they take you for the visit plus the report.
My most frequent shop requires about 25 minutes in the store and about 10 minutes to do the report. With the drive time involved, I figure these shops take an average of 45 minutes even when I am doing a route of them, so allowing 15 minutes each for the unexpected, I need to plan on spending an hour of my day on each shop. (Examples of unexpected: the company web site crashes periodically taking my report with it, I have a flat tire, the checkout line in the store is unexpectedly long, I circle the parking lot looking for a parking place, there are issues in the store such as an employee is too diligent in looking for an answer for me, the restrooms are closed for cleaning, I slip on a wet floor and management is not about to let me leave without filling out an accident report even though I protest I am 'just fine', I am going between stores and a funeral train of 60 cars is ushered out of the church parking lot in front of me and creeps along at 5mph through a long section of road where there are no side streets for me to duck into and go another way.)
On any route of shops I would strongly encourage you to do no more than one 'new to you' shop. This allows you to focus on the specific requirements of that shop so you don't miss anything. Shops you have previously done you should have some comfort with already, so your major issue with them is making your notes once you leave the store so you don't get them confused. Good notes keep you from worrying at report writing time that the blonde cashier may have been at the State St. location rather than the Main St. one.