This paper investigates the nonstabilizerness (magic) of random Matrix Product States (RMPS) and introduces Clifford enhanced Matrix Product States (CMPS) as a new class of quantum states. Nonstabilizerness is a key quantum resource that, along with entanglement, characterizes the non-classical complexity of quantum states. The study shows that RMPS, which have bounded entanglement scaling logarithmically with bond dimension χ, exhibit nonstabilizerness that converges to that of Haar random states as N/χ², where N is the system size. This indicates that MPS with a modest bond dimension are as magical as generic states. The paper introduces CMPS, which are generated by applying Clifford unitaries to RMPS. It demonstrates that CMPS can approximate 4-spherical designs with arbitrary accuracy. Specifically, for a constant N, CMPS become close to 4-designs with a scaling of χ⁻². The findings suggest that combining Clifford unitaries with polynomially complex tensor network states can generate highly non-trivial quantum states. The paper also discusses the properties of CMPS, showing that they inherit the 3-design property from the Clifford group. The 4-frame potential of CMPS is analyzed, and it is shown that the deviation from Haar states can be reduced by increasing χ. The study further shows that the purity fluctuations of CMPS are significantly smaller than those of stabilizer states, indicating that CMPS are closer to Haar states. The paper concludes that CMPS can be used to approximate 4-designs with arbitrary precision, and that the bond dimension χ can be adjusted to achieve this. The results have implications for classical simulation capabilities, as CMPS can be efficiently simulated using the Clifford tableau formalism. The study also highlights the potential of CMPS for tasks that require the computation of Pauli expectation values, such as determining ground states or simulating the time evolution of Hamiltonians.This paper investigates the nonstabilizerness (magic) of random Matrix Product States (RMPS) and introduces Clifford enhanced Matrix Product States (CMPS) as a new class of quantum states. Nonstabilizerness is a key quantum resource that, along with entanglement, characterizes the non-classical complexity of quantum states. The study shows that RMPS, which have bounded entanglement scaling logarithmically with bond dimension χ, exhibit nonstabilizerness that converges to that of Haar random states as N/χ², where N is the system size. This indicates that MPS with a modest bond dimension are as magical as generic states. The paper introduces CMPS, which are generated by applying Clifford unitaries to RMPS. It demonstrates that CMPS can approximate 4-spherical designs with arbitrary accuracy. Specifically, for a constant N, CMPS become close to 4-designs with a scaling of χ⁻². The findings suggest that combining Clifford unitaries with polynomially complex tensor network states can generate highly non-trivial quantum states. The paper also discusses the properties of CMPS, showing that they inherit the 3-design property from the Clifford group. The 4-frame potential of CMPS is analyzed, and it is shown that the deviation from Haar states can be reduced by increasing χ. The study further shows that the purity fluctuations of CMPS are significantly smaller than those of stabilizer states, indicating that CMPS are closer to Haar states. The paper concludes that CMPS can be used to approximate 4-designs with arbitrary precision, and that the bond dimension χ can be adjusted to achieve this. The results have implications for classical simulation capabilities, as CMPS can be efficiently simulated using the Clifford tableau formalism. The study also highlights the potential of CMPS for tasks that require the computation of Pauli expectation values, such as determining ground states or simulating the time evolution of Hamiltonians.