Total War: Shogun 2's second patch will add DirectX 11 support, as Creative Assembly stated they expect to release the patch in the first week of May. This makes sense since the recommended system specs state "AMD Radeon HD 5000 and 6000 series graphics cards or equivalent DirectX 11 compatible graphics card."
The second patch will also include multiplayer fixes: "Since Shogun 2’s launch, we’ve been completely blown away by the success of multiplayer. However, the multiplayer issues many of you have identified require our thorough attention, so that’s a really big priority as well. You can expect a raft of multiplayer fixes and modifications in Patch 2, and beyond."
We'll keep an eye out for the patch and host it here for your convenience.