Not sure the airlines have the control or ability to add a flight on a busy day as this involves airports and air traffic lanes (probably even more true with international flights where another government is also involved). (And I'm not talking about adding flights during a busy holiday weekend. It's just that Delta doesn't say: we're booked solid next Friday on flights from Detroit to Minneapolis, let's add a 2:30pm flight between the 1pm and 4pm flights.)
Rumor has it that flights are sometimes cheaper on Tuesdays and Wednesdays.
Make sure to check other cheap carriers who may not be in other search engines:
Southwest, Frontier and JetBlue.
Most search sites will have an option to also search airports within a certain radius of your point of origin and destination, and can also check fares a few days before and after. Make use of those.
Sometimes fares are inconsistent, for example, it may be cheaper if you fly into Baltimore and out of DC. It's still a "round trip" provided you start and end at the same airport.
Lastly, if you have no checked baggage, you can bail midflight. A friend was just looking at traveling to Detroit (one way) and the cheapest flight was one to Philly that stopped in Detroit (it was cheaper than just the first leg to Detroit. Crazy price models, eh?)