Carmichael numbers that remain "absolute pseudoprimes" in any given number field are known to exist. See

There are Inﬁnitely Many Perrin Pseudoprimes
Also, Carmichael numbers which remain "absolute pseudoprimes" in

*all* number fields up to a given degree are thought to exist, based on heuristics. However, this is only known to be true for degree 2. For examples in this case, see

HIGHER-ORDER CARMICHAEL NUMBERS