Here is an interesting site: www.xwordgrammar.com/
The site covers an alternative way of examining grammatical structures, which was developed by Dr Robert Livingstone Allen in the 70s. (en.wikipedia.org/wiki/Robert_Livingston_Allen)
What I found most interesting was not the methods for examining grammar, but the simple way that X-Word Grammar approaches sentence structures.
The site uses the terminology trunks, shifters, linkers and inserts to describe the way sentences are constructed.
A trunk is the main segment of any sentence, usually with the Subject-Verb-Object pattern:
Danny ate some cheese.
A shifter is a part of a sentence that can move about without affecting the meaning:
Before lunch, Danny ate some cheese.
Danny ate some cheese before lunch.
A linker connects two trunks together or two sentences:
Danny was eating lunch. Meanwhile, Penny was doing laundry.
Finally, an insert is used to insert extra information:
Danny, a big fan of brie, decided to buy some more cheese.
The basic concepts could be taught reasonably easily to an intermediate level class and would encourage them to think about the way they put sentences together.