foostring <- c("First test *** no asterisks at the end", 
               "Second test *** asterisks in the middle *** something different",
               "Third test *** more than one asterisk *** something different *** second asterisk ***",
               "Fourth test *** asterisks followed by a special character ***_something different")

gsub("\\*{3}.*?(?:\\*{3}|$)", "",  foostring)