Simple answer: fly internationally. Most (but not all) international fares permit stopovers of up to 24 hours. Domestic fares usually only permit 4 hour stopovers.

Also, this only works if the stopover city is part of a legal routing. For your hypothetical example of CLE-EWR-SEA, this probably wouldn't work. Looking at the legal routings for CLE-SEA, presuming there are flights that work, possible stopover cities might include DTT, CHI, GRR, and MKE, among others. Although this isn't a hard rule (there are always exceptions), generally speaking legal routings require you to be making some sort of forward progress towards your destination--thus, such a severe backtracking from CLE-EWR on the way to SEA is probably a no-go.