  This paper is a continuation of the papers J. Pure Appl. Algebra, 210 (2007),
437--445 and J. Algebra Appl., 8 (2009), 219--227. Namely, we introduce and
study a doubly filtered set of classes of modules of finite Gorenstein
projective dimension, which are called $(n,m)$-strongly Gorenstein projective
($(n,m)$-SG-projective for short) for integers $n\geq 1$ and $m\geq 0$. We are
mainly interested in studying syzygies of these modules. As consequences, we
show that a module $M$ has Gorenstein projective dimension at most $m$ if and
only if $M\oplus G$ is $(1,m)$-SG-projective for some Gorenstein projective
module $G$. And, over rings of finite left finitistic flat dimension, that a
module of finite Gorenstein projective dimension has finite projective
dimension if and only if it has finite flat dimension.
