In this paper, we are concerned with the multiplicity and asymptotic behavior of normalized solutions for the nonlinear mass-energy doubly critical Kirchhoff equation with mixed nonlinearities in \(\mathbb {R}^4\) . The mixed nonlinearities create a geometry of local minimizer, which makes the problem much more challenging and interesting in the Kirchhoff nonlocal and doubly critical setting. First, by combining the refined analysis for the geometry of local minimizer with the subadditive inequality, we prove the existence of the normalized ground states under more relaxed assumptions. Moreover, using the precise energy estimate and the perturbation method, we prove the existence of the second normalized solutions, known as normalized excited states of mountain pass type. Finally, the asymptotic behavior of the obtained normalized solutions is also explored. Some recent results from the literature are extended.
