First thing to note is that tensorflow will use all cores for processing by default. You have some limited manner of control over this via inter and intra op perallelism discussed in this authoritative answer:
Tensorflow: executing an ops with a specific core of a CPU
The second point to note is that a session is thread safe. You can call call it from multiple threads. Each call will see a consistent point-in-time snapshot of the variables as they were when the call began, this is a question I asked once upon a time:
How are variables shared between concurrent `session.run(...)` calls in tensorflow?
The moral:
If you are running lots of small, sequential operations you can run them concurrently against one session and may be able to squeak out some improved performance if you limit tensorflow's use of parallelism. If you are running large operations (such as large matrix multiples, for example) which benefit more from distributed multi-core processing, you don't need to deal with parallelism yourself, tensorflow is already distributing across all CPU cores by default.
Also if your graph dependencies lend themselves to any amount of parallelization tensorflow handles this as well. You can set up profiling to see this in action.
https://towardsdatascience.com/howto-profile-tensorflow-1a49fb18073d
