Yes. Apply the filter in the Action that defines what happens when the menu is clicked.

1) Activate the Developer Mode

2) Navigate to the menu you want to modify the filter for, for example top level Purchases --> Purchase --> Quotations

3) From the debug menu, select Edit Action.

4) Modify the Domain Value.

(In this example, the filter is applied to the purchase.order model to show only those documents that are not open purchase orders. If you look at the filter for the next menu down, the Purchase Orders menu, you will see the OPPOSITE filter. Both menus provide access to the same documents, but with mutually exclusive filters.)

My suggestion is to use a Record Rule: Record Rules allows you to define filters (domains, to be more precise) to happy to a Group.

This means that you need to create a custom Group, assign it to the user, and set record rule for that Group.