Easiest way to solve this will be probably creating a news streams which can reflect all activities of these subspaces.
It will not all show on the Activity page, but you'll have a link by hand on the Activity page to click on.
You can create up to 10 corporate news streams which is nicely explained in following document:
Or you can help the space manager to create a personal one. Let him start of by clicking the '+' sign.
And follow more or less the same steps as described in the above mentioned document.