Laundromat has 12 washers of which only 9 are in use. There are three 4" cast iron standpipes that the washers drain in to (4 washers in each standpipe). The three standpipes connect to a 4" cast iron drain line with trap (trap is not removable). It is unknown what or where the drain line connects to the main drain line as the line is in a wall and under a cement floor. When 5 or more washers are in use, soap suds and water (sometimes) will backup and over flow in one or two of the standpipes. The drain goes into a basement and the floor drain in the basement will also backup causing a mess. The amount of water and suds in the floor drain can range from a very small amount of wetness around the drain to 2 gallons of water and suds that have to be sucked up with a wet/dry vac. Laundromat is not routinely monitored and is left unattended most of the time.

Any ideas what could be causing the backup?

The three standpipes connect to a 4" cast iron drain line with trap (trap is not removable). It is unknown what or where the drain line connects to the main drain line
Are you saying that in place of installing a trap on each stand pipe the [plumber installed a running trap,(see image) in the branch? And the job passed inspection? There's no doubt that you have a ppartial blockage.
My bet would be the running trap. How are the stand pipes vented?
Snake the line from the standpipe and see if that helps. Good luck, Tom

Are you saying that in place of installing a trap on each stand pipe the [plumber installed a running trap,(see image) in the branch? And the job passed inspection? There's no doubt that you have a ppartial blockage.
My bet would be the running trap. How are the stand pipes vented?
Snake the line from the standpipe and see if that helps. Good luck, Tom

The trap is a "U" shaped cast iron pipe in the branch and has no access points. The only access besides the standpipes is at the end of the branch. None of the standpipes are vented that I can tell. I assumed that with 3 standpipes, one of them would act as a vent.

The branch is located approximately six feet above the floor drain so I don't understand how a partial blockage in the trap would affect the floor drain. I think you are on to something in that the standpipes are not vented. Reason being, when the floor drain was backing up, I cracked open the cleanout in the floor drain and I could hear it sucking air and the drain did not overflow. I will snake the branch and trap just to be sure - can't hurt but I think it is the non-venting. Any idea on how would I vent it?

Since the floor drain backs up This would be the first place I would snake. You have a partial clog downstream from it. I would also send a snake down the stanbd pipe past the running trap. Your stand pipes are venting inside the building through the stand pipes themselves.

when the floor drain was backing up, I cracked open the cleanout in the floor drain and I could hear it sucking air and the drain did not overflow
You may have two blockages. One in the branch that stops the standpipes from venting, hence the air being su7cked through the floor drain clean out, and another downstream from the flooe drain causing it to back up..
I have put in Laundromats but I've plumbed a them lot differently. Good luck, Tom

You've been very helpful and I appreciate your time. Thanks