While twins of the nonidentical kind can't become conjoined, they can become something called chimeras. This is where fraternal twins fuse together very early on in development. The end result is not two separate, connected people but one person with a mix of both twins.

Are chimeras more likely to have twins?

Chimeras Aren't More Likely to Have Kids with Chimerism

Even when the ovaries or testes of a chimera are made up of cells from both “twins,” their sperm or egg cells will only get DNA from one “twin” or the other. This is due to a process called meiosis.

Can a human be a chimera?

Human chimeras were first discovered with the advent of blood typing when it was found that some people had more than one blood type. Most of them proved to be "blood chimeras" -- non-identical twins who shared a blood supply in the uterus. ... About 8% of non-identical twin pairs are chimeras.