Next to the propellers you also have the LPC4300 series that have a Cortex m4 + Cortex m0 integrated.
However, those are "Application Proccesors", thus more designed for the m4 doing DSP or heavy lifting + the m0 running a protocol stack (serial, ethernet, USB, etc.) to accept commands.
If the goal is to complete multiple operations at once, you can look at interrupts obviously. They are probably the most important concept of any microcontroller, so it's important to understand them well.
A step further could be
CoRoutines; where a blocking event in a coroutine will jump out , and the next time the function is called resumes operation.
This has some limitations (like you can only do the blocking-escape inside the coroutine function) nor will it make your program very debugable (IMHO), so for bigger controllers you often find RTOS installed. RTOS have a pretty severe memory burden and some performance impact, but is an "easy way" to multitask on a microcontroller.
However, I wouldn't recommended installing a RTOS on any 8-bit controller.. they are too small for it to be of any use.