This morning, my wife and I were behind a SuperShuttle van near Reagan Washington National Airport. (They shuttle hotel guests from hotels to airports nationwide.
It had both Virginia and Maryland plates on it.
I’ve also seen semi-trailer trucks with several plates from various states.
My question is: why do these vehicles need to be registered in more than just one state?
Because they, in their normal course of business, use the roads in each of those states. The State says “You consistently use my roads for profit so you must pay my taxes.” The same is true for tractor trailers, except the metal plate on the trailer usually has the word “Apportioned” where the state name would appear. A sticker from each state where taxes have been paid is affixed to the cab.
The overwhelming majority of people have more than the average (mean) number of legs. – E. Grebenik
Well, ‘need’ is such a difficult word to deal with. The short answer is that they ‘need’ to do so because the law of the states within which they operate requires them to do so. That, of course, explains nothing of the reason for those requirements.
This isn’t quite accurate. As a user of a non-commercial vehicle, I might well use the roads of more than one state for profit (e.g. travelling salesmen). Nevertheless, I won’t be required to have a license plate in each state - indeed I will most likely be PROHIBITED from having one in each state.
The reasoning is more complex. Partly, it has to do with assumptions about commercial vehicles vs. non-commercial vehicles. It also has to do with agreements among the states and with the federal government about how to deal with ‘interstate commerce.’ Mostly, it has to do with the fact that each state wants to make as much money as it can off the fees generated by taxing commercial vehicles which use their roadways.
I doubt any answer could give you the ins and outs of a decision by a state as to when exactly to require a licensing by a commercial vehicle. Policy rarely is simple. 
My WAG is that it is not driven by the desire to get a piece of the interstate commerce pie. Rather, trucks put a lot more wear and tear on the road, and so they’re simply not allowed into the state without paying for the privilege.
Cars don’t do as much damage to the roads, but there are lots more of them, so I’m sure the states would like to charge the out-of-state cars as well, but it would face too much opposition, for several reasons: (a) Not enough room on a car for all the many plates someone might need. (b) Civil rights people would scream about restriction of movement. © Individuals would have to do a lot more planning for their interstate driving, whereas truckers don’t make as many spur-of-the-moment cross-country trips.