You cannot bring too much firepower to a gunfight. However, unless the fight is choreographed by a Hollywood producer you can only fire one weapon at a time. Therefore, to carry on the fight if the weapon you are firing such as a shotgun fails for whatever reason, jams, or runs out of ammunition you need to transition to another firearm, a handgun for instance.
If your shotgun fails and you are within handgun range then it is better to sling your shotgun and engage the enemy with your pistol. This may give you time to fix the jam or to begin a combat reload. You cannot allow the aggressor to advance on your position as you fiddle with a jammed weapon. You need a sling to maintain control of the shotgun. If you do not have a sling, you have drop the weapon to engage properly with your handgun. You really do not want to give up control of the shotgun if it can be helped.
To make yourself a smaller target crouch as you sling the weapon to begin the transition. One hand should be pushing the shotgun barrel down between your knees so the barrel is not banging on the ground or tilting you off balance because the muzzle struck the ground. The other hand is reaching for your handgun.
Practice crouching with the shotgun slung and then notice how the muzzle will hit the ground if it is along your side. You need to get the muzzle where it is not dragging or banging into you, so pull the muzzle between your legs.
If on the move sling the weapon as you move latterly to the shooter in a crouched position. Both hands have a function one is to secure the shotgun while the other brings the pistol to bear. It is difficult to shoot on the move with a slung weapon unless you have it across your chest or even across your back. You have to lower and rotate your shoulders to fire on the move and this is made more difficult because of the shotgun on your shoulder.
Practice is important and make sure you practice with snap caps to protect the firing pin and for safety reason of course never practice at home with a loaded weapon. Some firing ranges are set up for transition drills so try to find one where you can conduct live fire exercises.
In addition to transitioning from your shotgun to handgun there may come a time where you do not have a second weapon and you may need to “pick up a weapon”. The military and certain other organizations may train certain individuals to pick up weapons. Some shooting competitions also employ this tactic. The shooters start out with their own weapons and advance through several drills. Then they are instructed to shoulder or holster their weapon and pick another weapon up, and engage the targets. The sequence is timed. The pick-up weapon is made available during training and competitions. The weapon is loaded and is not the same type as the shooters started with. The pick-up weapon may be holstered on an injured person or laying on the ground or some other likely position from being dropped during a firefight.
This teaches shooters to use whatever resources are available during a firefight. It is not likely you as a homeowner would need to do this to carry on the firefight but you would need to secure the intruder’s weapon on your person if they drop it or they are injured to prevent them from using it again.