You can have the following special conversations at the HQ with the 
corresponding characters:

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. 
While in HQ: S.H.I.E.L.D. Command, speak to Mr. Fantastic as Iron Man. 
While in HQ: S.H.I.E.L.D. Command, speak to Maria Hill as Iron Man. 
While in HQ: Stark Tower, speak to Iron Man as Captain America. 
While in HQ: White Star, talk to everyone as Captain America.