The Machine turns up Coulson's number because mumble something in his past or S.H.I.E.L.D. related, so Reese starts to follow him. Turns out, Barton is also following Coulson because he has unrequited feelings and must protect.
Reese and Finch suspect Barton, then Reese and Barton team up to protect Coulson. Huge Bonus if Reese and Barton have a history, maybe a one-night stand when Reese was an agent and Barton was in the military in Afghanistan, maybe just UST and drinking/fighting/co-mission from back then.
Somehow Team Machine and Barton save Coulson. Somehow Finch learns that Reese is gay or bi from this and makes his move. Somehow Barton makes his move on Coulson. The two couples are happy and have hot sex, or fade out before the sex if you prefer. Or a foursome, if you can make it work, but I don't really see that, because of all the feeeeeelings.
Crossover with Avengers: Finch/Reese, Barton/Coulson
Reese and Finch suspect Barton, then Reese and Barton team up to protect Coulson. Huge Bonus if Reese and Barton have a history, maybe a one-night stand when Reese was an agent and Barton was in the military in Afghanistan, maybe just UST and drinking/fighting/co-mission from back then.
Somehow Team Machine and Barton save Coulson. Somehow Finch learns that Reese is gay or bi from this and makes his move. Somehow Barton makes his move on Coulson. The two couples are happy and have hot sex, or fade out before the sex if you prefer. Or a foursome, if you can make it work, but I don't really see that, because of all the feeeeeelings.
Before or after movie as you wish.