It is not hard to imagine that, from Disney's perspective, a "stay" is the one for which you have a dining plan reserved. The second reservation (even if linked) is likely to be considered (again, by Disney's sharp-pencil boys) a new "stay".
Of course, no one at Disney seems to care if you use years-old mugs, so it is not like someone will stop you. But, when loopholes become widely-known, Disney has been known to close them. So, if you insist on treating "stay" in a way that benefits you, my best advice is: enjoy it while you can.