Is it possible to define Magento layout updates on a per-store basis

Question

I have a single Magento install running two different websites. One sells ebooks and the other not and so the business team would like to see the "My Downloads" link removed from the customer navigation block in the My Account area of the application.

I can see the link defined in design/frontend/base/layout/downloadable.xml but cannot see any way defined that would let me disable the link on just one of the websites. Obviously, I could override this XML to turn off globally but I need the change to be limited in scope.

How do you define layout overrides on a single website or store in a multi site Magento installation?

Based on the responses below, I have done the following:

Created app/local/Mage/Customer/Block/Account/Navigation.php and added a method removeLink() which is not in the core code.

If I make the following change in local.xml, the download link is removed:

<?xml version="1.0" encoding="UTF-8"?>
<layout>
    <default>
        <remove name="catalog.compare.sidebar"/>
    </default>   
    <customer_account>
        <reference name="customer_account_navigation">
            <action method="removeLink" translate="label" module="downloadable"> <name>downloadable_products</name></action>
        </reference>
    </customer_account>
</layout>

But, if try to target a specific store, it is not. E.g.

<?xml version="1.0" encoding="UTF-8"?>
<layout>
    <default>
        <remove name="catalog.compare.sidebar"/>
    </default>
    <STORE_mm>
    <customer_account>
        <reference name="customer_account_navigation">
            <action method="removeLink" translate="label" module="downloadable"> <name>downloadable_products</name></action>
        </reference>
    </customer_account>
    </STORE_mm>
</layout>

Answer 1

As Anton suggested, set a new layout theme for your store. Another approach for anything site-wide + store-scoped would be to use the store layout handle - it's like a <default> handle which is applied each store. If your store code (under Manage Stores > Store View) is 'foo' the store layout handle would be <STORE_foo>.

Ref. Mage_Core_Controller_Varien_Action::addActionLayoutHandles()

Answer 2

Create different themes for this websites.
Create app/design/frontend/default/website1/layout/local.xml
and app/design/frontend/default/website2/layout/local.xml
Where you can make changes needed for downloadable layout. This is described in magento feature.