I have a Miche (Campy) 13 - 28 cassette with a Compact Double front crank. I love the 28 for climbing but am missing the high end of an 11. If I were to change the small cog for an 11 tooth, would I have problem shifting from the 11 to the second ring (14).

Yep. Modern cogs are designed to sit next to the cogs you buy them with.

BTW, 'rings' are on the crank.

exactly, you'd have to replace the 14-tooth cog with another 14-tooth that was designed for use next to an 11-tooth.

As usual, Sheldon tells all, his article deals with Shimano ones rather than Campy, but the basic problem and solution should be the same

https://www.sheldonbrown.com/k7.html (read the bit about custom cassettes, there's a link at the top of the article)

As for it not actually working at all, I've been running a cobbled-together cassette on an MTB for a while, some of the cogs are not designed to work with the ones they're next to, so they do shift rather badly, but it works.

Why? Pedaling at 105 rpm with a 50-13 you can go 32mph. With the 11 you can hit 38. You can get a good paying job riding your bike if you can keep that up. https://www.jbarrm.com/cgi-bin/c42strt.cgi

It may shift, if may even come close to being smooth, but that would be a huge jump from one gear to the next. You may be better off with an 11-28 cassette to get more even gear spacing. If you're talking 10sp Campy, IRD makes just such a beast.

I agree, just pedal faster. A shift from 14 to 11 would be horrible.

Yeah, massive gap.

Thanks for the advice, I am dropping the idea, I'll just pedal faster.