You can create a calendar where clients can book themselves in for meetings, sessions, etc. with Sprout Studio. We call this feature "Schedulers". A scheduler is where you'd set how long the meeting/session is and when it's available to be booked.
You can limit the number of slots booked on a day in the "Advanced Availability" section of your scheduler under the "Maximum Available Per Day" toggle. Keep in mind, that this is the maximum amount of slots that can be booked on a day. If your availability doesn't have the capacity to have more slots, then you might not actually hit the number you specified.
For example, if you said you can book 8 people maximum per day, but your available time slots only work out to allow 6 people to book, then 6 is the max that day.