Hi,
Yes that could potentially be done via some custom code. Creating a new mass action plugin which is adding specific triggers.
In this plugin, once the weekly trigger is called, do the desired checks and call the new triggers based on the data.
For example this plugin must add triggers like "every weds" and "every friday". And has a main function based on the trigger "onHikashopCronTriggerDays". That way it will be called every days, and there you can do the checks and if the day is Wednesday so call the trigger "every weds", if friday call "every friday" else, return false.
Then create two other mass actions, one based on the "every weds" trigger and the other one on "every friday" with the desired actions.