In this paper, using a generating function approach, we derive several new convolution sum identities involving the Fibonacci m-step numbers. As special instances of the results derived herein, we obtain many new and known results involving the Fibonacci, Tribonacci, Tetranacci, and Pentanacci numbers. In addition, we establish some general results providing insights into the inner structure of such convolutions. Finally, we state some mixed convolutions involving the Fibonacci m-step, Jacobsthal, and Pell numbers.