Possibly for as long as we've had electric vehicles, folks have been thinking up ways to charge more quickly or more conveniently. A common idea is to charge the car while driving, such as a gasoline engine or battery pack on a trailer. The built-in battery pack would be large enough for the typical day-to-day around town driving - perhaps offering 100-150 miles range. Then for longer trips you'd head to a rental place to rent a trailer giving more range, and somehow the car would be able to charge while driving. For the cost of a short-term rental, you could have a 300-400 mile range.
Something like this:
The concept is straightforward. You build a trailer with either a generator, or battery pack, possibly with solar panels, and tow it behind your electric car. A connection would be made between the trailer and car to allow charging while driving.
The advantage is in keeping the purchase cost lower. Some electric car makers advocate for large battery packs with 300-350 miles range along with a fast charging system allowing for a 1-1.5 hour recharge time from empty. While that combination erases most folks range worries, how often do most of us require a 300-400 mile driving range?
A more modestly priced car with 150 miles range would satisfy the large majority of drivers. And a range extending trailer could offer the longer driving range when needed.
A similar idea is to have a small onboard gasoline generator, that could perhaps be rented on a temporary basis. Having the range extension inside the vehicle, rather than as a trailer, simplifies the user experience since most of us are unfamiliar with towing a trailer. See Why do all-electric cars not have a small (efficient) generator for a limp home to ease range anxiety?
The primary issue is safety measures in the standard charging port.
Car manufacturers design electric car charging ports to prevent the car from being driven while charging. The idea is to prevent drive-off's. Forgetful people sometimes drive their car while the gasoline hose is connected to the car (and might even forget to pay the cashier). The manufacturers wanted to prevent this scenario with electric cars.
That means the solution is more complicated than to simply snake a charging cord from a trailer to the charging port. The car won't be able to drive.
The solution would require cooperation from the electric car maker, so that the charging trailer can bypass that safety mechanism. This is not impossible, and it raises an interesting efficiency gain. Charging from the extender battery pack could be DC rather than AC, circumventing the efficiency losses due to converting from DC to AC only to convert back from AC to DC in the on-board charging system.