A good speaker system is a balance of cabinet, drivers and crossover; you can spend a lot of money trying to get a certain sound out of a cabinet designed for a different one. I suspect better drivers and crossover would improve the sound but just what it would sound like is anyones guess and I doubt it would be identical to a Response 3.
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I agree with Stanwal. And as a former Response 3 owner, I think that you would be just as happy with something else. My Response 3s (MSRP, $6500) couldn't hold a candle to my Gallo Reference 3s (MSRP, $2600 at the time I bought them). But if you're doing this mostly for the fun of it, by all means have at it :-)
Those Proac Response 3s are great sounding speakers. I have recently assembled a pair of the Parts Express Kits and I think they may be better. It is just hard to tell because it has been a while since I listened to the Response 3s. I remember getting them in on trade and keeping the for over a year. The Dayton Kit is pretty killer.
The answer to your question is that you can buy and install parts in the existing cabinets to (more than likely) get better sound than what you have now. To duplicate the sound of the Proac is probably not realistic. Unless you have them for comparison side by side. There are a number of sources online where folks who have practiced the art of speaker design for a long time share their designs for free to people looking to DIY stuff.
Everything linked below can be purchased from http://www.madisound.com
Troels Gravesen's CNO-25 uses very nice components (I can vouch for that, my speakers currently use the same drivers)
Zaph Audio's ZRT 2.5 way (scroll to the bottom of this page) has drivers that a lot of people feel are some of the best around. The air circ tweeter and the scan speak 8531 midbass drivers. I built this speaker for a friend of mine, he is thrilled with it.
This one may not meet your criteria because of the smaller woofers. Very, very nice drivers. Not sure on the crossover implementation as I have not heard this design:
There are lots of options. I've only touched on a few. It would take a little research to compare your enclosure size to ones needed for the builds I listed above. Just some food for thought.
I know nothing of how Proac built Response 3's. I'd be willing to help if you can get a crossover schematic.I've been in Speaker Building for over 30 years. I do have 1 MTM that I believe is better than the Proac. Problem is 4 ohm and 86db. The are tube tolerant, but obviously, you'd need some juice to run them. If you are interested send me a private email and I will give you more scoop,