Some form of this thought is irresistible, but we shouldn't hesitate to point out the obvious flaws. You load up your car with more people and more stuff when you go on a trip, and more batteries would add MORE load on the frame. This doesn't work. Ideally, you would add another axle.
Suspend disbelief and follow that thought to its logical conclusion.
You have almost certainly PLANNED your trip. You know what time you will depart, and the trip may take 4 to 10 hours, done in a single day. Additionally, you will spend 30 minutes packing your car, and more space is a premium. Keep following me, just a little bit longer..
The day before you depart at, say 3pm, a worker from an established car rental service pulls up in front of your house and parks on your street. They unhitch a trailer from their car, do some technical checks, and are gone in 5 minutes.
You arrive home from work, and have a trailer that will add 400 miles of range to your car and offer extra packing space (for things). You pack up the trailer & car and go to bed. In the morning, as you pull out, you get out and hook up the trailer.
Depending on your trip, you may charge up the car & trailer once, or not at all. I'm guessing that it will be able to connect two chargers at once.
This seems like not-a-bad-idea, and compatible with current infrastructure. While it incurs a cost, and requires EVs to be built for the purpose, it's a much more minor change than battery swapping. The cost could be quite small compared to the other solutions for the same problem, and it frankly sounds more direct.