I think you need to disambiguate "adding".
If you mean actually modifying dimensions, then it can be done through custom rules but it's not going to be great (and the user would likely have to be an admin). There are Marketplace solutions to cater to that sort of scenario, like Application Control Manager - which formalizes the process for users to request metadata changes. I guess some folks would just allow users to access the Dimension Library page that administrators typically use, but the security implications are very significant. Generally speaking, regular users are not meant to modify the structure of data - they are meant to upload data and analyze it.
If you mean just visualizing different members that already exist in a dimension but are not currently displayed, then it's very common through the use of Parameters. Instead of using a text box, you'd have either a proper Member Selector triggered from a Button (which already provides search capabilities, among other things), or a Listbox with the multiple-selection option set to True. Both would be bound to a Parameter, and then that Parameter would be used in the CubeView to define which rows should be shown. You'd have to refresh the Dashboard containing the Cube View to see the change, which can be done automatically on Button or Listbox components.
You might want to look at the Design and Reference guide for more info, or get the OneStream Foundation Handbook from Amazon.
