Preheat oven to 350 degrees F.
In a food processor add the cream cheese, mayonnaise, and Dijon and blend until smooth. Then add the lemon juice and olive oil, if desired, and season with salt and freshly ground black pepper. Process until well combined, scraping down the sides with a rubber spatula as you go. Dump the mixture into a large mixing bowl and fold in the chopped chives and crabmeat. Adjust seasoning with salt and pepper then cover and set aside in the refrigerator.
For the crackers:
Meanwhile, prepare the saltines. Make a garlic butter by combining the minced garlic with parsley and melted butter. Lay out a flat layer of saltines on a lined baking tray and use a pastry brush to baste the saltines with garlic butter. Bake in the oven for about 5 to 7 minutes until golden.
Split each tomato lengthwise and toss in a mixing bowl with balsamic vinegar. Toss the cherry tomatoes on a second baking tray and drizzle a little olive oil, if desired, over the top. Season with salt and pepper and bake in oven for 7 to 8 minutes.
To serve, arrange the 3 components so they can be assembled by each individual. Spoon the crab mixture into a bowl, stack the saltines in a pile next to it and serve the roasted tomatoes in a coffee cup. Take a saltine, spoon a little crab dip on top and garnish with a piece of tomato.