Any person who has fourty percent (X) of the vote gets to be president. If one person gets sixty percent (Y) of the vote, they get to be the only president.
Thus if the population is united behind one president (say in wartime), it can be. If the population can't agree on its president, then there are several presidents.
When there are several presidents, a group of citizens gets selected randomly. The General (s) come in and say should we march Left or Right. President a says left and President B says right. The citizens then vote. Would urgent decisions get decided better this way? Assume that our early warning system detected missiles coming our way? Would a group of citizens be better able to decide whether to fire before the missiles come in first or wait and see if it is a glitch or false positive. Google books (Moral Principles and Nuclear Weapons by Douglas P. Lackey) has reports of early warning systems going off due to geese and the moon as well as later on due to computer glitches. Fortunately, these were all detected by human analysts. (One certainly could conceive of a sortition jury selected and specifically exposed to how our early warning systems work. Brian Martin in his 1995 article on "Demarchy" proposes specialized sortition groups.)
Note that we can allow continual voting rather than elections. That is, when citizens get tired of a President, they can change their vote. Some presidents might promise to only focus on one area of policy (say domestic, crisis handling, financial) This allows the people to choose (Should one of the presidents campaign on a platform of limiting their actions to a specific area, the people could vote to remove him.)
Note that I propose allowing continual voting. At any time a person can go down to their local Elections office and change their vote for president. Also, individuals can select their own number for the x and y, the thresholds for a President to loose their position or to be the only president. The percentages would only change a while later or be restricted to move giving us a hysteresis and preventing changing the percentage to be used instead of just voting in or out a particular popular or unpopular president. High school civics classes (timed just before people turn eighteen or whatever the voting age is) would go over the history of the presidents and their popularity. Then, the high school students upon registering would enter their values of x and y which would go in to the median value. (And of course when a voter dies, their vote would go out of the calculation.)
Power sharing can have problems. Combining it with sortition is an answer to these problems.