The outcome of William Howard Taft's failed attempt to expand the Open Door policy deeper into Manchuria primarily led to increased tensions in the region, particularly between Japan and China, but it did not lead directly to any of the options listed. However, if we have to select one from the given options, the most closely related outcome would be:
• It caused Japan to go to war against China and Russia over control of Manchuria.
While Taft's policies themselves did not directly cause the war, they contributed to the broader geopolitical tensions that existed in East Asia during that time. The actual conflict, known as the Russo-Japanese War, occurred in the early 1900s and was influenced by the competing interests of these powers in Manchuria.