You will have to work very hard to overdose
Several studies have shown that the majority of Americans are deficient in potassium. A healthy person would need to eat 700 to 800 bananas a day to get enough potassium each day from that source alone. However, too much potassium can be as dangerous as too little, as it can destroy the heart muscle. For a healthy person to reach that danger zone, they would need to eat 400 bananas a day! If someone ate too much potassium from bananas, their stomach capacity would stop them before they got sick.
In general, eating two bananas a day is a good idea for any healthy person. People taking beta blockers for heart disease should be careful, as beta blockers raise potassium levels. Diabetics may not want to eat bananas twice a day because they are considered "medium" on the glycemic index. Otherwise, go for it! Research indicates that a high potassium intake reduces the likelihood of death from any physical ailment by a solid 20%.