The factory mats have a plastic insert which fits into the holes and secure
by turning the "plug" half a turn. I think you would have to be extremely
luck to find a mechanism which would fit the BMW floor plug. Maybe you could
go to a dealer and look at how the stock mats are attached, but I doubt you
would be able to adapt anything to it.

You could always just use some Velcro fasteners to keep the mats in place.

As an aside, I looked at all kinds of aftermarket mats and found that the
BMW mats not only looked great (color and fit) and (obviously) fit
perfectly, but they were also priced very competitively with any aftermarket
product.