Can having an iron-deficiency anemia cause me to have other deficiencies also?

Depends on the cause. Usually not. However, it will depend on the cause of course .Having an iron deficiency anemia will not cause you to have other deficiency. However, if the reason why you have iron deficiency anemia is due to gastric by pass surgery or gastric removal surgery or autoimmune gastritis for instance- then you can have both iron deficiency as well as vit B12 deficiency- because of absorption problems.
Maybe. Iron deficiency can be caused by several different things. Some may lead to other deficiencies. In your situation, the cause of iron deficiency is important to better answer your question.