Sure. Just pick obscure enough airports. The list of airports covered by the Essential Air Service program (government subsidies to maintain air service in communities where it otherwise wouldn't be profitable) is a good starting point, since those airports usually have limited connectivity.
So picking basically at random, we could start at Del Norte County Airport in California (CEC), which has one flight a day seven days a week to/from Oakland (OAK). We could travel to Tupelo Regional Airport (TUP) serving Tupelo, Mississippi, which only has flights to/from Nashville (BNA). So if we could fly CEC-OAK-BNA-TUP, that would be a 2-stop itinerary, but the only direct OAK-BNA flights are sold by Southwest, which does not interline with Contour airlines. In this case, it's possible to fly from CEC to TUP with only two stops, but not possible to book a single itinerary.
But if we pick different airports, we can find even more difficult ones. Start at CEC again but travel to L. M. Clayton Airport in Montana (OLF), which only has connections to Billings (BIL). There are no nonstop flights from OAK to BIL. The only way to fly between CEC and OLF, short of your own plane or a charter, is to fly a route with more than two stops, like CEC-OAK-SLC-BIL-OLF. That's a route that also can't be booked on a single ticket.
I'm not aware of a tool for finding such city pairs besides picking airports that are likely to have poor connectivity. The OpenFlights database could be a good starting point if you wanted to automate the process of searching for such city pairs yourself, but the routes data is out of date. Putting cities into FlightAware can help too, to find current flights between two airports regardless of airline.