I think the big picture is missing - Cadillac used to be the standard of the world (back in 1909, but it still counts

). Now it's doing fine in America, but certainly not in the world. Cadillac needs a better lineup to compete on a global scale.
What I would suggest:
1.
DRAMATICALLY IMPROVE QUALITY - better materials, fit and finish
2.
DESIGN - STRIKING BUT REFINED - as mentioned before, CTS (and other models too) does not LOOK like a premium car. It surely does stand out both inside and out, but that's not the point here. Audis are probably less "striking", yet there's something about the refinement and cleanness of their design, the thoughtful dashboard layout and attention to detail that makes them unmistakeably premium cars.
3.
ATTENTION TO DETAIL ONCE AGAIN - this concerns the entire car, nothing overlooked. Cadillac ought to have all the features the others have and preferably more - remember they were the first brand to offer "crankless ignition"? Why are they to do without keyless ignition? Cadillacs have to be extremely well-thought, practical and convenient in everyday use and suprise owners with small and seemingly unimportant solutions and details.
4.
MATCH PRICE AND SIZE - for example, CTS is almost 5er-sized (or GS, E-Klasse, S-Type et al.), but price-wise it's in the territory of 3er, IS and the like. "More car for the buck" works well with family cars, but not with prestige automobiles. CTS needs to be on par with either group in terms of quality, size and price. You can't convince people to forgo their 3ers becuase they can get a bigger car for the money (they could have a dozen others, but somehow they chose the 3er), or a 5er buyer to save up on the STS - the people buy BMWs or Mercs because they can afford them, not because they are bargains.
5.
FOCUS AND DON'T STRETCH BEYOND REASON - although many premium brands ventured into new areas lately, it benefits their volume rather than image. If Cadillac started it's revolution around RWD, it should stay that way. There's no need for small FWD sedans, compact crossovers and the like - leave that for other brands, which GM has in abundance. A RWD small midsize car to compete with IS/3er might be advisable, but provided it's RWD. This could be either a downsized CTS or a brand new model. And nothing BELOW it.
6.
NO NEED FOR HYPEREXPENSIVE SUPERSHOWCAR - as the Maybach and Rolls-Royce ventures show, the market for superexpensive cars is very small and unpredictable. Although a car like that might boost Cadillac's image and egos of a few GM bigwigs, it can also be a costly flop, which is just what GM does not need. There's enough room to expand for Cadillac - e.g. models to truly rival S-Klasse, CL, A8, 7er, 6er etc.
6.5.
NO NEED FOR 12, 16 CYLINDERS - 12-cylinders are heavy and the benefits over modern-day V8s are usually outweighed by, well, the weight, which impedes handling, as well as fuel consumption. BMW and Mercedes top models garner better reviews in V8 than V12 versions, and the former outsell the latter by a bigger margin every year. Just look at the emphasis all the manufacturers pay to their V8, while the V12s remain largely neglected. A new engine block would cost a lot and have very limited use. GM would better develop a big brother for the Northstar out of existing engine blocks.