We prove a generalization of N. Ozawa’s Kurosh-type theorem to the setting of free products of semiexact
II
1
\text {II}_1
factors with respect to arbitrary (non-tracial) faithful normal states. We are thus able to distinguish certain resulting type III factors. For example, if
M
=
L
F
n
⊗
L
F
m
M = LF_n \otimes LF_m
and
{
φ
i
}
\{\varphi _i\}
is any sequence of faithful normal states on
M
M
, then the
l
l
-various
(
M
,
φ
1
)
∗
.
.
.
∗
(
M
,
φ
l
)
(M,\varphi _1) * ... * (M,\varphi _l)
are all mutually non-isomorphic.