Not all bases will fit on all K bikes. I think the K1100 has a larger tank. It is my understanding that the K75 and 100 bases will interchange. The K1100 base will not fit the baby brick or the 100. I can not speak with certainty about the K1, but I have seen somewhere that it fits the 1100 bikes. Also, the zipper that fastens the base to the tank bag was changed during production so not all bases will fit on all bags. Early bags sport a fine zipper with heavier zips later in production. I do not remember exactly when the zipper was changed, but will post the information after I look it up.
Take note that there are about four, maybe five, different styles of the tank bag made over the years. The newest version has a flat top and the outside is all black including the trim. I think the one before it was black with a small amount of yellow trim. Earlier tank bags were different colors. With that being said, the tank bag itself seems to be interchangeable from bike to bike, if you have the correct base with matching zippers. My dealer offered me a complete new K1100 set up plus a base for my K75. You do not want to know how much that was going to cost me.
Do you already have a base and/or bag? If you can live with an aftermarket bag, you can get some very decent bags for the same amount (or less) as a used OEM bag.