Singular links of almost metastable dimensions

The objects studied are singular links of $p_1$-,$\dots,p_r$-, $p$-spheres in the $n$-sphere. A theory of such singular links for $\max\{p_1,\dots,p_r\}<2n/3-1$ and $p<3n-3\max\{ p_1,\dots,p_r\}-5$ is constructed. The theory generalizes (as far as it is possible) the theory of singular links of $k$-,$\dots,k$-, $p$-spheres in the $(2k+1)$-sphere, where $k>1$, developed in the author's recent papers.