When I was apprenticing at a corporate catering business I was put on the sandwich station for awhile. This was one of the busiest jobs because a lot of our business was for lunches. My boss was very particular about her tuna salad mixture. It couldn't be too wet or dry - just the right amount of mayo. We made huge batches every day and you had to get it just right.
She added onion, salt, pepper, lemon juice, mustard, hot sauce and Worcestershire to it. Then it was layered with lettuce, tomato, pickles and more S&P. To be honest I thought this took away from the tuna but it was a popular sandwich.
When I make tuna salad for TB, I add some of his eggless soy free mayo (tastes surprisingly good), green onion and dill (fresh when I can). Oh and a little salt and pepper just because he likes it that way.
When we were eating regular mayo I usually tried to make my own. It doesn't last long but is oh so good.