Unable to find a ComboBox component for that would work in an Ext Grid, permit multiple selections, and support both local and remote datasources with multiple fields (one for display, one for the index), I set out to build my own some time back.
Jump right to the download or view more technical details and examples below.
Example of the Ext JS MultiSelect ComboBox
Here is an example of the MultiSelect ComboBox.
Example of the Ext JS MultiSelect Combobox a Grid
Here is an example of the MultiSelect menu working in an Ext JS Grid.
Technical Details
The source for the examples above is pretty self explanatory, feel free to post in the ExtJS forums with any questions as I will lurk there.
Caveat
The one major drawback with this component is that it currently does no paging, either locally or remotely. So if you are working with a long list, the list may extend outside the scope of your page. This is a pain and I invite any solutions, I will happily update my code and provide a credit to anyone who contributes a working solution to this and any other buggy behavior I have not noticed.
I have also noticed a minor behavior bug - the first item in the list is always selected after the list is displayed, and must be de-selected. Strangely, this bug does not act up when the MultiSelect is used in a grid, but elsewhere it does.