At the moment, if your board permissions are ‘only edit items or subitems that users are assigned to’ you cannot create subitems under your item, unless you are a board owner.
This doesn’t really make sense, as if you can edit the contents of an item, you should be able to add subitems for these. Use cases include different SLA dates for different departments working on the same ticket. This is currently unavailable in monday, and would really help with making sure that collaborative tickets are completed in a timely manner without the help of an additional board or opening up permissions.