In a large bowl, add the tuna, reserving the olive oil in a separate small bowl. Break tuna into bite-size pieces with a large fork. Add the beans and capers. Into the bowl of olive oil, add the red wine vinegar. You should have 1 part vinegar to 2 parts oil - add more extra-virgin olive oil if necessary. Season with salt and pepper. Pour dressing on the tuna, bean and caper mixture and allow the flavors to infuse while slicing the vegetables. Add the onion and tomatoes to tuna mixture and toss gently.
Place the arugula on large decorative platter and top with tuna mixture. Tear fresh basil leaves over the top and serve immediately.