March 15 (Reuters) - Activist investor Engine No. 1 raised the stakes in its proxy fight with top U.S. oil producer Exxon Mobil Corp on Monday, urging shareholders to not only vote for four of its own nominees but also against four current directors. Engine No. 1, which counts pension fund California State Teachers’ Retirement System (CalSTRS) among its top supporters, said it is asking shareholders to vote against the re-election of Exxon directors Steven Kandarian, Douglas Oberhelman, Samuel Palmisano and Wan Zulkiflee. (Reporting by Shariq Khan in Bengaluru; Editing by Krishna Chandra Eluri)