This paper investigates a novel class of bounded symbols for the Toeplitz operator acting on a Bergman space for unit disks. We introduce and rigorously study quasi-biharmonic symbols, which generalize classical biharmonic functions while preserving essential analytical properties for applications in operator theory. Our main theoretical contributions characterize the commutant for the Toeplitz operator with symbol φ(z) = zm + |z|2αg(z) and φ(z) = |z|2ng(z) + h(z), where g is analytic, and h is harmonic. Using advanced techniques from complex analysis and operator theory, including polar decompositions and Mellin transform methods, we prove that under appropriate regularity conditions, any Toeplitz operators that commute with Toeplitz operators having such a quasi-biharmonic symbol must be linear combinations of the identity operator and operators with the quasi-biharmonic symbol. These findings significantly extend existing literature on commute problems for Toeplitz operators and provide new theoretical insights into the algebraic structure of the Toeplitz algebra on the Bergman spaces.