Honestly all this talk about pushing for more than one prize has me a bit uncomfortable. Aside from lowering our chances of getting any prize at all, has anyone considered that it might make us look... arrogant or grasping?
I mean look at it from the perspective of the clanless: They have a once in a lifetime opportunity for a real goddamn chance to change their lot in life. They're already facing stiff competition, then the Goketsu - already an influential clan with a seat on the council and significant social connections, despite being made up of foreign traitors - take two of the prizes, because they aren't satisfied with their existing influence, they aren't satisfied with that plus no taxes and getting 10 million ryo per year for the rest of their lives, no, they also want 10,000 acres of land on top of that!
As for the clans: To them this is supposed to be something of a friendly competition (I mean not exactly, you don't make the prize pool for your office fantasy football league $100,000 after all). The clans will recognize that to a certain extent, they all benefit from cooperation in that so long as nobody really goes for broke, all the clans can make significant and meaningful contributions - without giving up all that much themselves - and simultaneously satisfy the Hokage and take home a nice prize on top of it for their patriotism. In come the Goketsu who don't seem to get the point (from the clan's perspective) and pull out all the stops to try and take home multiple prizes! And not only that, these jumped up traitors seem to honestly believe that they can split up their contributions and still win twice over!
All I'm saying is that, while trying for two prizes may not be against the letter of the rules as presented, it certainly seems to be against their spirit. And while I don't imagine Asuma will be particularly cranky (especially if our contributions are good enough to win twice over), I do believe that a move like this will strain relations with pretty much everyone else who wants to put in anything more than token competition.
Once again, imagine how this plays out in real life. Suppose that, in the 40 yard dash, instead of running through the finish line and celebrating his victory, Usain Bolt turned around and sprinted back to the starting line and made it back before the bronze medalist finished. Do you not think that might engender some hostility from his fellow olympians?