I don't know if this is relevant at all, but my gaming group once played a short adventure that we called "THE GAME". Loosely inspired by some old CT JTAS contact or adventure that I read where some NPC dies and hands something to a player's character.
In THE GAME, every player had a character and every character had TWO generated character identities. In one identity, the character was a member of a secret organization ... from law enforcement to corporate security to a contract hit man. In the other identity, the character had a 'cover' that he was using. There were several cross plots going on - an attempt to steal a prototype, a political defector, that sort of stuff. What tied them all together was being on a large commercial liner travelling from one port to another. To make matters just a little more interesting, since every character had access to an intelligence network of one sort or another, I generated a matrix for each character of who every passenger claimed to be and what their security organization uncovered about that character. Some covers survived the security check, some partially held and just turned up something suspicious and some were broken, revealing who the character really was.
In actual play, each player had to play along with both their false identity and the identity that each other passenger claimed to be. At the same time, every player was aware that at least some of the other players were aware that their character was not who they seemed ... but who was a natural ally, who was a natural adversary, who had nothing to do with you?
This setup generated a need to play on two levels at all times. The players needed to communicate openly with the referee and other players about what was obvious, and secretly with the referee and sometimes just one other player about what was happening in secret.
Secret communication was most often handled by passing notes to the referee. Players sometimes heard (and enjoyed watching) events that they needed to keep their characters ignorant of. There was a strong element of 'the honor system' required (which is what I would expect of a group of friends gathered to have fun). Technology assisted in throwing a surprise or two into the game when one of the players had to leave, but continued to play by calling in to get an update and set a bunch of "If this happens then my character does that" scenarios.
Specific advice to help with your game ...
1. It is not practical to keep the players from knowing that SOMETHING is going on, so be open, mature and friendly about it. Everyone should probably be willing to let a player have some special fun with the expectation that the favor will be returned if their character has a similar opportunity/need.
2. Pass notes. Do not underestimate the usefulness of communicating 'what ifs' to the referee to invoke as needed.
3. Back in the day, we had phones ... today, you have iphones that can send and receive text messages. High tech notes might be an option.
4. You are correct that some times, the Ref and player may need to step out for a secret moment. See #1 and the group should understand.
Hopefully, some of that will be helpful.