Rust does have shared mutability, often called interior mutability, which allows mutation through a shared reference. Here's some documentation on the topic. Getting used to this concept can be easier, in my opinion, if you mentally substitute some phrases:
When you read
Think of it as
Mutable reference
Exclusive reference
Immutable reference
Shared reference
Interior mutability
Shared mutability
This shared mutability lies behind the concurrency types which allow you to get a &mut, like Mutex and RwLock in addition to the Cell types and Atomic types. It's also implicitly present in other places, like when you allocate something with a clone or write through a &File.
Ahhh right! Now I remember a video I've seen from Jon Gjengset on YouTube where he said that you can count Mutex also as one of those types! Anyways: Thank you very much for your kind help folks!