OWD,
OK...we're talking doubles here...not pistols...Belgium, not Germany, not England

Only big outfits had enough drop forges to supply a production line...eventually Pieper and ML dominated the trade...ML was a publicly owned company and supplied forged recievers and other small drop forgings to the almost the entire Liege double gun trade...including many, many makers in France, Spain, and Italy.

you asked;
What is a finishing house? Are you saying that most of the big-name retailers were just finishing off guns that were being made by the trade?

No, the big name retailers bought the guns from the finishing houses...example...Shoverling, Daly, and Gales and VL&D bought their guns from finishing houses like Francotte.

Finishing houses like Francotte and Lebeau bought their materials(receivers and small forgings) from the publicly owned ML...ML not only supplied these foirgings all across the trade, they also had massive finishing departments...this is exactly the anomaly that gets collectors confused...

also...ML produced many guns with the Cockerill name...Cockerill was a barrel manufacturer that was either a subsidiary or was absorbed by ML. ...if I remember correctly, they were at the same street address...54 Rue somthing?

It's not that hard to gain perspective when you realize that the Liege shotgun trade was primarily 3 large outfits. One privately owned, and 2 publicly owned. the largest was and still is FN...all three had their own finishing departments...nearly all the other finishing houses got their ebauches or materials from ML...

after that, the finishing houses, and the varying degree in which they utilized the cottage labor force, gets a little complicated.