well, since you want to apply this to the total shipping, you cannot do this on the shipping tab of the eCart object. to do it on the shipping tab would create an endless loop, since eaxh time the shipping is calculated, it would end being recaculated.
you can do this on the charges tab though.
set the calculation of the charge to a flat rate and use the following code:
$this->GetShipping() * $_SESSION['yourSession']
where yourSession is the name of the session you create that contains the multiplier.