I got the UA 30k, CO 50k, a 2nd Marriott Premier 50k and a PC Select 60k all within a 6 month time frame. At the time of opening these, I already had a Marriott Premier and a Slate which is a byproduct of countless transformations since I opened it as a college card back in 1990. All of these are Chase products.
As one other FT'er has said, YMMV.
Peace!