I have been using The Dow Blue foam as well as white bubble polyurethane foam, mountains in minutes other wise known as insulating foam sealant in a can and all these can be glued together with liquid nails. not only will it glue all foam together when it dries it sucks the pieces together in a very tight bond. in fact Liquid Nails was originaly designed as a FOAM BOARD ADHESIVE and cleans up with soap and water until it has dried for more than 5 hours after that your not going to remove it from anything including your hands.
For the best bond spread a very thin layer on the two pieces you want stuck together and then stick the two pieces together and align them where you want them to stay come back in 8 hours and they are as one piece even gluing 4x8 foot sheets edge to edge or end to end.
Rio Grande Dan