My parish has only had 4 scheduled Masses per week for the last year. More often than not, Masses were cancelled at the last minute so the 4 scheduled became 1 celebrated.
Canon law says that a priest cannot accept more intentions than he can celebrate in one year.
Can. 953 No one is permitted to accept more offerings for Masses to be applied by himself than he can satisfy within a year.
I don’t know how that translates to how many the parish can accept because in parishes such as ours it’s not always the same priest who celebrates these Masses.
What I remember from my youth is that, at least once a year, Mass stipends would be forwarded to the Missions to be celebrated and a list of Mass intentions that had been transferred would be posted at the back of the church for all to see. My present parish has been the recipient of such transferred Masses at the request of the pastor when our parish’s Mass book was empty.
With us it’s feast or famine. Few people make a habit of requesting Masses. In fact, unless things have drastically changed since I left the office 18 months ago, only 4 people make a point of requesting Masses on a regular basis. So, unless someone popular dies, there is usually lots of space for a last-minute request, although without a secretary that has become more difficult since, instead of weekly, Mass intentions are announced a month in advance.
While the average person is lucky to get 2 or 3 Masses offered for the repose of their souls, more popular people get 50 or more. Unless a specific date is requested or we are low on requested Mass intentions, we usually schedule only one Mass per person per week. That means that in a year where we have the death of a couple of well-known and loved parishioners, if you’re one of 50+ people requesting a Mass for the same person, you’re unlikely to see it celebrated until a year or more after you request it.
Now that we have a Pastor again (he arrived yesterday) we will probably have more Masses each week.