Roundtrip and one-way should be fine. There may issues with cached inventory or fare filings. You can check actual fare bucket inventory with an ExpertFlyer account or for free on the BCDTravel website (https://flightavailability.bcdtravel...MnAvlMain.aspx).
I should add that the multi-city fare issues have to do with combining multiple segments on a single fare (so searching for flights with a 4 hour connection or less domestically, or 24 hours internationally). If each segment is on a different date, you generally shouldn't run into issues. Each segment will fare individually in this case (since they can't be combined on a single fare) and checking inventory on the individual flight segments is the correct behavior. There's some exceptions to this (Hawaii fares often allow stopovers between islands, for example).