A surge protector can have multiple outlets. However, it is not always advisable that you fill in every outlet. This is because you could trip a breaker, which means disconnecting the circuit. This is especially important when you are using a surge protector on large devices such as heaters and TVs. Therefore, limit the number of large devices on one surge protector. But if you’re only plugging in smaller items, such as phone chargers and an alarm clock, it would be safe to fill all the outlets because the amount of power used is low.