Changing your own email address is usually enabled by default. See this entry in portal.properties (or override -ext.properties in your portal)
field.editable.com.liferay.portal.model.User.screenName=administrator,user-with-mx,user-without-mx
field.editable.com.liferay.portal.model.User.emailAddress=administrator,user-with-mx,user-without-mx
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