Is it possible that 3 different kinds of vaccine can be given at one time?

Yes: This is commonly done and effective. Many, many studies have shown the body can make excellent immune response to multiple vaccine challenges given simultaneously; even young infants create long lasting antibodies in this way. Furthermore, our bodies handle it well though a sore arm or leg, low grade fever, or generalized aching, certainly tells us our body is working to build new immunities.

Yes: Depending upon the vaccines, there is ample research demonstrating safety of doing so.