What degrees are higher than a PhD?
There's no strict hierarchy. Every degree has a specific purpose or meaning, so sometimes a degree will completely eclipse another, but this is not always the case. 

The PhD is a research doctorate. It specifically means that someone has performed some worthy amount of original academic research in their field, and would be qualified to conduct further academic research on their own. This requires a high level of general understanding in the field, and in fact most degree programs will require students to have the equivalent of a master's degree before they propose their dissertation. For these reasons the PhD eclipses earlier degrees like the BA, BS, and MS. 

Professional degrees are a good example of degrees that are orthogonal to the PhD. For example, the MD specifically prepares someone to practice clinical medicine. Another, the JD specifically prepares someone to practice law. There are lots of people running around with MD-PhDs and JD-PhDs. Sometimes the PhD is a PhD in Law or a PhD in Medicine, but often it is not- someone with a JD and a PhD in Chemistry or Computer Science could make a very good living at the frontiers of intellectual property law.

Someone with a MD-PhD doesn't have a "higher" degree than a PhD, they have two separate degrees that each describe a single specialization. There are people with PhDs but no MD who do research in medicine, but an MD-PhD brings together the medical training and the research training in one person, and hopefully better understands the medical issues presented than the only-PhD does.

Generally the PhD is a terminal degree in any field in most countries, meaning there is no degree that builds upon the PhD the same way that an MS builds upon a BS.

The UK is notable for having a system of "higher doctorates" and "junior doctorates" though I'm not sure exactly how the system there works in practice (I'm from the USA). Every country does things a little differently based on tradition, but the UK seems to do things a little differently a little more than most. 

https://en.wikipedia.org/wiki/Doctorate#Higher_doctorates

Some cursory Wikipedia browsing suggests that the UK's higher doctorates are somewhat honorific in nature, and would be considered equivalent to a PhD in the US system. 

There are lots of US universities that offer oddball degrees, like an S.J.D. in law, but most of these are designed to be equivalent to a Ph.D. in practice. My guess is that they keep the old degree titles out of a combination of tradition and uniqueness.

https://en.wikipedia.org/wiki/Doctor_of_Juridical_Science