We consider the existence and multiplicity of normalized solutions for the following equation with the nonlocal singular term and local generalized perturbation term: \(\begin{aligned} -\Delta u+\lambda u=\mu (I_\alpha *|u|^{p})|u|^{p-2}u+f(u),\ x\in \mathbb {R}^N, \end{aligned}\) where \(N\ge 3\) , \(\frac{N+\alpha }{N}<p<\frac{N+\alpha }{N-2}\) , \(\mu >0\) , \(\lambda \in \mathbb {R}\) arises as a Lagrange multiplier and \(f\in \mathcal {C}(\mathbb {R},\mathbb {R})\) possesses several weak \(L^2\) -supercritical conditions that eliminate the requirements for homogeneity and \(\mathcal {C}^1\) regularity. By carefully analyzing the intricate interplay between nonlocal Choquard-type and local nonlinearities, we establish different variational geometries of the above equation. In order to avoid complex topological arguments, based on the more general minimax principle on the manifold, we show that when \(\frac{N+\alpha }{N}<p<\frac{N+\alpha +2}{N}\) , there are two solutions to the above equation, one is a local minimizer with negative energy, and the other is Mountain-Pass type. When \(\frac{N+\alpha +2}{N}\le p<\frac{N+\alpha }{N-2}\) , we prove that the aforementioned equation has a ground state solution with Mountain-Pass level.
