The regex crate doesn't support it, and it's not something I'm personally interested in working on. My goal at this point is to make the regex crate as good as possible at what it does, across the board. There's still a long way to go.
Other than that though, there is a WIP crate that actually builds on the `regex` crate and provides fancier features: https://crates.io/crates/fancy-regex (Created by the same author as Xi.)
You can also use bindings to a more established library. The Onigurama bindings seem well developed: https://github.com/rust-onig/rust-onig
There are also bindings to PCRE, but they are of varying quality. The regex crate's benchmark suite binds to several other libraries (including C++ and D libraries), but they are very minimal bindings sufficient for rough microbenchmarking: https://github.com/rust-lang/regex/tree/master/bench/src/ffi