You could try roasting your meat of choice then using the drippings added to a roux (equal parts butter and flour cooked) then add cream (or dairy of your choice) Makes a simply cream gravy. If you start with the roux you can change things up adding herbs. If you are looking for variation in sauces, it really would depend on the meat. Like skirt steak beef is nice with a black and pink peppercorn cream gravy with mushrooms! Or if you want something lighter you can have a peppersteak sandwich with a light Au jus.
-your traditional herb mixture like rosemary, thyme, sage makes them a touch more exciting. Though it depends on the meat
-Adding lemon zest, capers, olive oil to the gravy makes it a touch meditteranean
-For italian you can add sausage sweet peppers and parsley to some simply gravy
-caramelized onions, steak sauce, blue cheese makes a super rich sauce for steak
-for a tropical touch, adding crunchy cashews, mangoes/pineapples and chili garlic sauce makes a great sauce for chicken or fish
For a chinese touch you can usually buy some oyster sauce and mix it in some chicken stock after a stirfry. Use the cornstarch slurry after your sauce has been reduced a bit and you have some great gravy. Even better if you add escallions and garlic
These are some I can think of right now.