Re: 3 or 4 eggs per cell
Drone laying queens ( I have only seen two ) tend to lay single eggs per cell, looks great but all drones.
Laying workers tend to "lay a pile " of eggs per cell.
Once, I placed the laying worker hive over a double screen board over a queen right hive for awhile, then shook the LW hive out.
I have alsoAdded queen cells to a hive with a drone layer queen, which resulted in no moredrone eggs, but no mated queen either... Finally donated a frame of eggs & they actually made a queen cell, returned a mated, laying queen. by this time the hive had dwindled , desperately , not enough bees to cover the comb of a single . ( I swaqpped locations with a stronger hive, I really need to super that hive ... tomorrow. After 5 monthes.
Shake them out, then after a couple of weeks split your other hive with a purchased queen.
Good Luck ... CE
Started summer of 2013, just another new guy, tinkering with bees.