I call this a "quad roller" because it has two more jewels than a traditional double roller.
I'm repairing (unmangling) and servicing a LIP R184 balance wheel electronic in a nice Waltham. This movement has one roller jewel to advance the driving wheel (which has magnetic detent) directly, a second one in double roller configuration to run a traditional looking lever that does nothing except restrict the balance to +/- 1 rotation (this lever has cool magnetic banking), and a third to nudge the contact wires to turn the impulse coil on at the right moment.
The LIP technical manual for this movement uses the word "peculiar" over and over when describing the operation. I really like working on oddballs like this.