You can have the following special conversations at the HQ.

As Daredevil, talk to Black Widow.
As Invisible Woman or Human Torch, talk to Mr. Fantastic.
As Jean Grey, talk to Cable.
As Spider-Man, talk to Green Goblin.
In HQ: Whitestar, talk to everyone as Captain America.
In HQ: S.H.I.E.L.D Command, speak to Mr. Fantastic as Iron Man.
In HQ: S.H.I.E.L.D Command, speak to Maria Hill as Iron Man.
In HQ: Stark Tower, speak to Iron Man as Captain America.