Thread:Project:Support desk/Hook to modify text of transcluded page

I need a way to remove the first line of an article or template that is being transcluded. I was using InternalParseBeforeLinks and preg_replace to accomplish my goal, but I encountered a corner case in which a parser function is being executed with transcluded text before InternalParseBeforeLinks is executed. As a result, bad input data (i.e. the first line of the transcluded article) is being passed to the parser function. Is there some equivalent to an "OnTransclusion" hook?

Thanks in advance.