Ignoring any "Well, it depends..." type answers (which aren't necessarily wrong, but neither are they necessarily helpful), the best answer I can come up with is: "By performing value-add activities which cannot be performed more efficiently and effectively in other areas of the business, and the performance of which does not impact current PMO performance"
Let's expand on that a little. Taking the last part first, you have no business (without prior approval) changing the services that you provide for the worse in order to do something else in addition. So you might reasonably review what you do to see if some things can be done more efficiently (or perhaps not at all) without damaging the business in some way.
So now you have an idea of the resource, in terms of capability and numbers, which you can apply to new areas of activity. Remembering that most PMO activity can be classified under one of: administration, control and guidance, consider which of these is an appropriate target area for the resources at your disposal. Bearing in mind that this is also an opportunity for development, don't be afraid to set your sights on a 'stretch' objective. You may be able to change the assignments of a number of individuals in order to free up resource for more ambitious (and, probably, more value-add) activity than would otherwise be the case.
The first part of the answer is intended to point out that just because something could or should be done, the PMO may not be the most effective centre for the activity. For example, establishing trends in the comparison of business cases with actual business outcomes may not be appropriate if there's a business performance department which may have access to more data and can bring greater analytical power to bear.
So what might you be able to achieve? Rather than provide a list of candidates, I've identified a few areas which may contain opportunities:
What are your thoughts?
To get in touch feel free to contact Richard Bateman on 01908 283600, email RBateman@citi.co.uk.
Julie Black is Associate Director at Project Management Group, and kindly provided this article in July 2015.