Can someone with activated (in use) Sharingan be pulled into a genjutsu by another person with activated Sharingan? I mean, I know Itachi was able to do it to Kakashi, but Kakashi only has (er, had) one Sharingan, not two. So, I guess my example would be if Itachi and Sasuke were fighting, both with their Sharingans blazing, could one pull the other into a Genjutsu just like they could do to anyone without Sharingan, or does both users having their Sharingan activated cancel it out? I can't find any information on this despite looking for a few hours!
Yes they can do that.
The best example for it is probably the final fight between Sasuke and Itachi where the whole first part of it was just a genjutsu.