I know that for some people this may seem like a weird idea.... but remember....similar things actually happened in the past.
At a certain time in the 80/90´s there were SEGA games published on the NES, like After Burner, and SNK games published on the SNES, like Samurai Shadow. Both companies had their own consoles at that time.
I don´t think that it would be much benefitial for Sony, though. We all know that Vita is suffering hard in the West, but in Japan the situation is not that bad....... Could Sony studios maybe launch 3DS versions of its games just for distribuition in the West, maybe ? Still, if they do that, they would just decrease their chances of selling more Vitas because it would lose the advantage of exclusive content....
On the other side, it´s hard to tell if 3ds owners would really engage in buying Sony games. It seems that only Japanese developers can do well on the 3ds, like Capcom, Namco, Atlus, etc.
If Vita sales do not get better, they could experiment with the possibility