RAW no apart from looting a corpse of the your dead champion or specialist or the master crafted route as above described.One loophole is buying a Master Crafted version of the same weapon. You're allowed to stash a weapon if you replace it with one that is Master Crafted. Bit expensive way..
Most of the House specific weapons are fairly middle tier for thier use and similar types are available at the Trade Post. Suppression laser is essentially a shotgun. Enforcers shotguns and bolters are basically normal versions but better ammo rolls. So a lot of them can get the rough same use.
Thematically however, the vehicles that the gangs use are custom made rigs made from scrap and subjected to incredible abuse. Ash storms are nasty. These buggys roll and get trashed regularly. Would you bolt a tank of lethal chemicals to a roll cage and careen around the wastes like a maniac? You would rather trust a foot slogger to care for the expensive gun.