The development of conventional, silicon-based computers has several limitations, including some related to the Heisenberg uncertainty principle and the von Neumann "bottleneck". Biomolecular computers based on DNA and proteins are largely free of these disadvantages and, along with quantum computers, are reasonable alternatives to their conventional counterparts in some applications. The idea of a DNA computer proposed by Ehud Shapiro's group at the Weizmann Institute of Science was developed using one restriction enzyme as hardware and DNA fragments (the transition molecules) as software and input/output signals. This computer represented a two-state two-symbol finite automaton that was subsequently extended by using two restriction enzymes. In this paper, we propose the idea of a multistate biomolecular computer with multiple commercially available restriction enzymes as hardware. Additionally, an algorithmic method for the construction of transition molecules in the DNA computer based on the use of multiple restriction enzymes is presented. We use this method to construct multistate, biomolecular, nondeterministic finite automata with four commercially available restriction enzymes as hardware. We also describe an experimental applicaton of this theoretical model to a biomolecular finite automaton made of four endonucleases.