Objective: The paper recovers cubic–quartic optical solitons with the Sasa–Satsuma equation that includes a combination of third-order dispersion and fourth-order dispersion effects to address cubic–quartic vector solitons for the first time. Methods: Two integration schemes are applied to catch out the solitons to the newly structured model. They are G′/G–expansion scheme and modified Kudryashov's approach. These pave way for a full spectrum of vector solitons. The recovered vector solitons are enumerated after a revisiting the mathematical strategies. Results: The mathematical approaches retrieve the dark, bright and singular vector solitons to the model. These solitons are presented by virtue of the certain restrictions. Rational and singular periodic solutions are also emerged with the mathematical schemes. Conclusion: Cubic–quartic vector solitons are yielded for such a model in this work for the first time. This would naturally lead to further ventures in this area. The newly structured model would be to address to recover the conservation laws. Other natural extensions to the model would be to consider with DWDM topology that would also lead to soliton solutions and their respective conservation laws.