I replaced a Shimano 11x24 cogset with a 12/28 cogset (12/14/16/18/21/24/28). If I put enough tension in the cable to move from 12 to 14, the next click causes the chain to shift from 14 to 18. (Similarly, in shifting outward, the chain skips from 18 to 14.) Decreasing the cable tension removes the skipping phenomenon, but then I can't shift from 12 to 14.
I thought maybe the chain was moving too far outward when shifting onto the 12 gear (thereby requiring too much cable tension to move it back inward onto the 14 gear). But I've set the limit screw so that the outward movement is as little as possible.
Here's something that may be relevant. Both cogsets have seven cogs. But when putting on the new cogset, I couldn't screw on the lockring that came with it. I had to use the lockring from the old cogset.