Can you modify the My Site v4.master that users will receive and their My Sites will be created from it when they create My Sites?

Hello Community

    Using SharePoint 2010 Server with UI, a web application was
created and then subsites.

    Modifying a site v4.master is not a problem even though you
have to modify the master for every subsite you created because
you can't create a template for that purpose because you can't
modify the names of template to reflect it new purpose.

    The problem comes when you create My Sites.

    The problem is that there doesn't seem to be a way to modify
a  My Site v4.Master then if you could when there are large numbers
of users you can't be there to change their masterpage
when you create their My Site.

    Is there a way to modify the My Site v4.master so that
when users create their My Site they get the modified version
that you create?

    Thank you
    Shabeaut