I have no idea how I didn’t know this: Delta is one of only two US airlines to permit free stopovers on award tickets entirely within the United States (Alaska also allows stopovers on domestic awards, which I just learned now while researching this). United will charge you an extra 10,000 miles for a stopover. American only allows stopovers on international itineraries (and even then, only at the international gateway city). US Airways only allows on international awards (and theoretically only at Star Alliance hub cities).
Even better, you can book these online, saving yourself a few dollars from having to call their call center.
Sure, it may be a wee bit difficult to actually find low level awards on 3 legs for your trip. Also, you cannot have a stopover and an open jaw (something to keep in mind if you live in New York and were looking at flights that depart from LaGuardia and return to JFK).
Here’s how it’s done:
Step 1: Go through leg-by-leg and determine which flights have availability at the low level. WRITE DOWN EACH AVAILABLE FLIGHT.
Step 2: Laugh maniacally when you can’t actually find 3 legs anywhere near the dates you wanted.
Step 3: Curse yourself for bulking up on Skymiles as you watch your friends with United miles flying hither and yon (or at least Yon — wait, is Yon in Micronesia?)
Step 6: Delta will return a list of flights for the first leg with, unhelpfully, no indication about whether they are available at the low award level. That was why we had you WRITE DOWN EACH AVAILABLE FLIGHT in Step 1.
Step 7: You’ll do the same thing for the next 2 legs of your trip.