The authors define an infinite sequence of symplectic capacities, which they believe agree with a sequence previously defined by the second author [K. Siegel, “Higher symplectic capacities”, Preprint, arXiv:1902.01490]. They provide a combinatorial description of their invariants on all \(4\)-dimensional convex toric domains. Their sequence is defined for Liouville domains in terms of pseudoholomorphic curves, without using virtual perturbations, as the minimal energy of a \(J\)-pseudoholomorphic curve satisfying some tangency condition, and then taking the maximum over all choices of almost complex structures \(J\). They extend the definition to symplectic manifolds by taking the supremum over embedded Liouville domains. Calculation of these invariants in examples leads to some sharp obstructions for stabilized symplectic embeddings, i.e., symplectic embeddings \(X\times\mathbb{C}^N\hookrightarrow X'\times\mathbb{C}^N\).