Yes, It is possible to have twins by IUI. In fact, ones have 10-15% chance of pregnancy by IUI. There is a 5-10% chance of having twins from this method. The common twins found in IUI are dizygotic twins.
As IUI starts by ovarian stimulation, it is possible for women to have more than 1 egg, and thus have more than 1 child in one pregnancy. In addition, due to the stimulation, there is a likelihood that the embryo could split into twins, but this is not commonly found.
Nevertheless, there is only 1% chance of having triplets in one pregnancy, depending on the standard stimulation. Normally, the doctor will check through the monitor to examine the possibility of twins when the patients have too many eggs.
If ones have too many eggs, the doctor will postpone sperm injection or prohibit sexual intercourse in that cycle to prevent twins pregnancy. Then, the doctor may adjust drug levels to reduce the number of eggs. The reason is because twins pregnancy has a high chance of miscarriage.
Reference: Prime Fertility Center Co., Ltd.