It's not impossible but it is unlikely. I've used David's to rent my DVC points three times. The way it works is I filled out a form telling him how many points I had available to rent. So you could contact them and ask whether the person you rented points from told David's they had more points to rent, then they could check availability at Poly.
For example, last year I wanted to rent 350 points because my youngest had just turned 2 and we weren't going back until he was 3 and a half (because you have to pay for airfare once they are 2+). So I had a lot of banked points and my full year 200 points for 2014 that I wanted to rent.
If I had done a rental for 200 points I still would've wanted to rent my additional 150. So in that case if David's had asked me if I could cancel the reservation and make a new one for more points I would have been really happy to do it.
So, as I said, it's worth asking. But I imagine most people tell Davids they want to rent X points and they get a deal for X points. I doubt most people have 300+ points available to rent like I did.
Another possibility is if the person you rented from doesn't have more points maybe they can still move the reservation to Poly for fewer days and then you can rent points from someone else to have a second reservation for your remaining days.
It's worth asking. It's a huge hassle and I don't think David's DVC Rentals wants to "bother" their DVC owners to change reservations so they may just say "no, it's final and we're not changing it". Don't blame them if they say that because their business depends on repeat renters and good word of mouth.
