Rinse cannellini beans until runoff is clear, drain 2 minutes and blot gently on a clean towel.
Drain without squeezing and separate into generous 1-inch flakes on a plate.
Halve tomatoes, dice cucumber, slice onion, chop parsley and drain capers; blot juicy vegetables.
Whisk lemon zest and juice, Dijon, garlic, oregano, salt and pepper, then stream in olive oil.
Fold dry beans into dressing and rest 10 minutes.
Fold in tomatoes, cucumber, onion, parsley and capers.
Scatter tuna over the salad and fold three to five times, stopping while large flakes remain.
Refrigerate 15 minutes; taste and adjust with lemon by the teaspoon, oil by the tablespoon or salt by a pinch.