There are actually recipes for caesar salads that include tomatoes. Usually they’re cherry tomatoes - the small, roundish ones that look like small cherries - but there are tomatoes in those salads all the same. These salads often include lettuce, and other odd things you may not usually think of putting on a caesar salad.
These might include anchovies and Worchester sauce. In fact, all of these ingredients are in a cherry tomato caesar salad shared from New York Times. A traditional caesar salad wouldn’t have tomatoes on it, but there are a few variations on this theme available on the internet. A quick search on the internet will turn up a lot of recipes for caesar salads with cherry or grape tomatoes, even sliced tomatoes.