You've never seen example.co.uk? Many countries use them because the top level domains for gov, edu, etc are restricted to one country.
There's two on the second page of active HN discussions, telegraph.co.uk and independent.co.uk.
Should we mention fourth-level domains, like ci.east-palo-alto.ca.us or stanborough.herts.sch.uk?
Those are not quite the same though, being something specific and short so essentially behave like a tld in their own right. For a long time you couldn't buy a <something>.uk, it had to be .co.uk or similar, so those _were_ the tld.
The way .name worked you could directly register <name1>.<name2>.name instead if getting <name2>.name and setting up <name1> as a subdomain. It meant john.smith.name and dave.smith.name could be completely separate registrations. You can't generally register <name1>.<name2>.tld like that.