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Derivatives of the commercial alloy CMSX-4 were directionally solidified and characterized with respect to their final dendrite microstructure. The results indicate that Ni-based superalloys with high segregation levels show significant instability in secondary dendrite arms and an increased tendency for tertiary arm formation, respectively. Phase-field simulations were used to explore the impact of chemical composition on morphological instability and tertiary arm formation during the directional solidification of Ni-based superalloys. It is found that an increase in specific alloying elements in the overall alloy composition leads to pronounced segregation at the end of solidification. This causes strong growth restriction of the secondary arms and triggers tertiary arm formation. The proposed mechanism explains experimental microstructures found in modifications of the base alloy CMSX-4.