If by user-defined pointers you mean arbitrary integer-to-pointer casts, then this is a kryptonite for static analysis, and I don't think you can have a languag

If by user-defined pointers you mean arbitrary integer-to-pointer casts, then this is a kryptonite for static analysis, and I don't think you can have a language that is both fast and fully predictable (UB-free) in their presence. It breaks pointer provenance and aliasing analysis, and existing compilers already struggle with such casts in C. But apart from that, you can have pointers, with many levels of indirection, as long as there are rules that prevent use-after-free, unsynchronized concurrent access, and other UB-worthy problems. Rust's borrow checker with rules for no mutable aliasing and Send/Sync markers for concurrent access comes close, but it has to give up on generality for safety (e.g. it can't reason about circular data structures).