A(M)C 20-193 specifies the objectives that are expected to demonstrate airworthiness of avionics that include multicore software based on software DAL. No objectives are indicated for DAL D systems, and only a portion of the objectives are indicated for DAL C systems, but this does not necessarily mean that related activities should be performed – see the corresponding FAQs below.
In the general case, the simplest path to certification of a multicore processor should be by addressing the applicable A(M)C 20-193 objectives. If you wish to use alternative methods of compliance, you should discuss these with your certification authority.