It took me a while to figure out how to do this, so posting in case anyone else is looking for the same.
A simple substitution works well:
sed 's/pattern.*$/&\n/'
Example :
$ printf "Hi\nBye\n" | sed 's/H.*$/&\nJohn/' Hi John Bye
To be standard compliant, replace \n by backslash newline :
$ printf "Hi\nBye\n" | sed 's/H.*$/&\ > John/' Hi John Bye