It's one of those questions that doesn't come up until there is a problem. The problem is usually a lack of progress in making ones profit goals, or a series of losses across multiple positions that causes a draw down that is larger than expected. How many positions should you have at one time? Today we will address this question with all types of market participants in mind.
The Day Trader: One who is so active as to day trade better have an extreme amount of comfort in their platform operation and trading computer setup to have many trades on at one point. A beginner should consider only having one on at a time until they are comfortable with all aspects of their strategy.
An experienced day trader will not question so much the number of trades. If there is plenty of opportunity the experienced day trader should be able to take advantage of all of it. If not then they will take what they can get.
The short term trader: If holding positions for a few days or weeks is your goal then you may find that you need to get comfortable with many positions on at a time. The turnover naturally associated with your style of trading may require more open positions.
A new trader will likely only wish to have a few open position on while looking for others to add. As far as the maximum number of positions it will depend on your risk per trade and your total account size.
The long term investor: This is one who is focused on finding growth in a company that can sustain the ups and downs of an economic cycle. Generally it is taught that a long term investor only allocate a small percentage of their capital to one position but what if there is a lack of "good" companies to invest in? You may consider starting a position with smaller size and adding over time, building an ever larger position all while keeping your risk in line.
It would never be suggested that a long term investor have one position on at a time. Even the most passive of investors still allocate over a few sectors and products.