Conditional Drop-down

Unfortunately Quickbase doesn't have a conditional multiselect like that. If you want to have multiple selections you will need to create multiple relationships and copy the conditional dropdown settings for each one so they all operate the same if you want to create a type of multiple selection. The gist is you have Selection (1), Selection (2), (3) .... until you reach the practical limit you want. 

For reporting you can create a formula multi-select that lists the selections made in your set of dropdowns if that's needed.