In the present paper, a description of overgroups for the subsystem subgroups
E
(
Δ
,
R
)
E(\Delta ,R)
of the Chevalley groups
G
(
Φ
,
R
)
G(\Phi ,R)
over the ring
R
R
, where
Φ
\Phi
is a simply laced root system and
Δ
\Delta
is its sufficiently large subsystem, is almost entirely finished. Namely, objects called levels are defined and it is shown that for any such overgroup
H
H
there exists a unique level
σ
\sigma
with
E
(
σ
)
≤
H
≤
Stab
G
(
Φ
,
R
)
(
L
max
(
σ
)
)
E(\sigma )\le H\le \operatorname {Stab}_{G(\Phi ,R)}(L_{\max }(\sigma ))
, where
E
(
σ
)
E(\sigma )
is an elementary subgroup associated with the level
σ
\sigma
and
L
max
(
σ
)
L_{\max }(\sigma )
is the corresponding subalgebra of the Chevalley algebra. Unlike the previous papers, here levels can be more complicated than nets of ideals.