Actually threads from several processes work

Question

In the Windows operating system with two physical x86 / amd64 processors (P0 + P1), 2 processes (A + B) work, each of which has two threads (T0 + T1), is it possible (or even ordinary) to see the following:

P0:A:T0 works simultaneously with P1:B:T0

then after 1 (or is it 2?) the context switch (es?)

P0:B:T1 works simultaneously with P1:A:T1

In short, I would like to know if - on a multiprocessor machine - the operating system can schedule any thread from any process at any time, regardless of what other threads from other processes are already running.

EDIT: To clarify a stupid example, imagine that process A thread A: T0 has an affinity for processor P0 (and A: T1-P1), while thread B of process B: T0 has an affinity for processor P1 (and B: from T1 to P0). It probably doesn't matter if these processors are cores or sockets.

Is there a first class context switch concept? Perfmon shows context switches in the Thread object, but nothing under the Process object.

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