Yes, you can do too much exercise. That said, it is impossible to generically determine how much is too much. This is because every individual will be able to handle different loads depending upon their fitness level, eating habits, genetic makeup etc.
Often the person that can best assess if you're overdoing it is yourself. If you feel excessively run down and low on energy, this could be a sign that your body is not handling the exercise load effectively. If you experience mood swings and are easily irritated, this is also a sign of fatigue. Some other more obvious signs that too much exercise is being performed may include a reduced quality of sleep, decreased appetite, affected menstrual cycle, injury, increased resting heart rate, increased blood pressure and depression.
Whilst additional exercise will often result in additional weight loss, if your weight loss is extremely quick, this poses many health risks. Risks may include gallstones, elevated blood pressure, high cholesterol, coronary heart disease, altered hormone levels, increased fatigue, increased disposition toward fat storage and depression.
The best advice I can give is to listen to your body. If you are experiencing any side-effects of excessive exercise, give your body time to rest and recuperate. Also remember that it is important to begin exercising slowly and build up gradually. This will allow your body to adapt to the increased demands.