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Given an $r$-graph $F$ with $r \ge 2$, let $\mathrm{ex}(n, (t+1) F)$ denotethe maximum number of edges in an $n$-vertex $r$-graph with at most $t$pairwise vertex-disjoint copies of $F$. Extending several old results andcomplementing prior work [J. Hou, H. Li, X. Liu, L.-T. Yuan, and Y. Zhang. Astep towards a general density Corr\'{a}di--Hajnal theorem. arXiv:2302.09849,2023.] on nondegenerate hypergraphs, we initiate a systematic study on$\mathrm{ex}(n, (t+1) F)$ for degenerate hypergraphs $F$. For a broad class ofdegenerate hypergraphs $F$, we present near-optimal upper bounds for$\mathrm{ex}(n, (t+1) F)$ when $n$ is sufficiently large and $t$ lies inintervals $\left[0, \frac{\varepsilon \cdot \mathrm{ex}(n,F)}{n^{r-1}}\right]$,$\left[\frac{\mathrm{ex}(n,F)}{\varepsilon n^{r-1}}, \varepsilon n \right]$,and $\left[ (1-\varepsilon)\frac{n}{v(F)}, \frac{n}{v(F)} \right]$, where$\varepsilon > 0$ is a constant depending only on $F$. Our results reveal verydifferent structures for extremal constructions across the three intervals, andwe provide characterizations of extremal constructions within the firstinterval. Additionally, for graphs, we offer a characterization of extremalconstructions within the second interval. Our proof for the first interval alsoapplies to a special class of nondegenerate hypergraphs, including those withundetermined Tur\'{a}n densities, partially improving a result in [J. Hou, H.Li, X. Liu, L.-T. Yuan, and Y. Zhang. A step towards a general densityCorr\'{a}di--Hajnal theorem. arXiv:2302.09849, 2023.]

Toward a density Corr\'{a}di--Hajnal theorem for degenerate hypergraphs