The number of online courses you can take depends on the specific type of program in which you're enrolled. Traditional schools that offer online classes usually place a stricter limit on the number that can be taken than do institutions that offer only online courses. At brick-and-mortar schools, you will likely have to get approval from an adviser to enroll in more than four courses (either online or in-person ones) for 12 credit hours per semester your freshman year. After that, you may need permission to take more than 15 or 20 credit hours per semester. These general requirements pertain to the pursuit of a bachelor's degree. If you are working on a master's, you can usually take up to nine credit hours a semester. Part-time students are allowed to enroll in one or two courses per semester.
Online universities may allow students to take more classes at once than do traditional colleges. But remember: Just because you don't have to physically attend an online course doesn't make the assignments and tests any less challenging, so don't overload yourself with too many classes. Be realistic about your capability and set your online course load accordingly.