The famous Bach Family (a very large family) used to get together and sing quodlibets or several songs at the same time. If anyone came to protest the “noise” they were invited to come in and join the fun. You all can do this too.
Try singing 3 traditional rounds at the same time (maybe start with just 2). Try “Frere Jacque,” “Three Blind Mice,” and “Row, Row, Row Your Boat” all together. Let me know how it goes.