Infinite loop space maps into or out of BAut(F_n) There is an inclusion $S_n \to Aut(F_n)$ from the symmetric group into the automorphism group of a free group. After applying the Quillen +-constriction, both $BS_{\infty}$ and $BF_{\infty}$ become infinite loop spaces and the map above can be promoted to an infinite loop space map $BS_{\infty}^+ \to BF_{\infty}^+$.

Are there any other infinite loop space maps into or our of $Aut(F_{\infty})?$

Some notes: 
1) Galatius has shown relatively recently that $BAut(F_{\infty})^+$ is homotopic to the sphere spectrum; the latter has been known for about 4 decades to be homotopic to $BS_{\infty}^+$ (Barratt-Priddy-Segal). So loop maps in or out of the symmetric group can all be defined up to homotopy on $Aut(F_{\infty})$ instead. Also, in all of the above, can "Aut" be replaced by "Out"?
2) Answers involving $\Omega^{\infty}S^{\infty}$ that don't relate to spaces of graphs or free groups don't count - I'm trying to get information on this from a geometric group theory point of view.
 A: Let $Aut(\bigvee^k S^n)$ be the topological monoid of pointed homotopy equivalences from a wedge sum of $k$ copies of $S^n$ to itself.  Then $Aut(\bigvee^k S^0) = S_k = \Sigma_k$. The fundamental group functor induces a homotopy equivalence
$Aut(\bigvee^k S^1) \simeq Aut(F_k)$. The $n$-th homology functor induces a homomorphism
$Aut(\bigvee^k S^n) \to Aut(Z^k) = GL_k(Z)$.  Suspension induced maps
$$
B\Sigma_k \to BAut(F_k) \to \dots \to BAut(\bigvee^k S^n) \to \dots \to BGL_k(S)
\to BGL_k(Z) .
$$
Here $S$ is the sphere spectrum.
Taking the wedge sum with the identity map on $S^n$ allows $k$ to grow.
In the colimit we get
$$
BS_\infty \to BAut(F_\infty) \to \dots \to BAut(\bigvee^\infty S^n) \to \dots
\to BGL_\infty(S) \to BGL_\infty(Z) .
$$
Taking the plus-construction and multiplying with $Z$ you get infinite loop maps
$$
Q(S^0) \to Z \times BAut(F_\infty)^+ \to \dots \to A(\ast) \to K(Z)
$$
where $A(\ast)$ is Waldhausen's algebraic $K$-theory of a point.  The
intermediate infinite loop spaces $Z \times BAut(\bigvee^\infty S^n)^+$
for $1 < n < \infty$ seem to be poorly understood.
An early reference:

Friedhelm Waldhausen, Algebraic
  $K$-theory of topological spaces. II.
  Algebraic topology, Aarhus 1978 (Proc.
  Sympos., Univ. Aarhus, Aarhus, 1978),
  pp. 356–394, Lecture Notes in Math.,
  763, Springer, Berlin, 1979.

A: In the following paper
U. Tillmann, The representation of the mapping class group of a surface on its fundamental group in stable homology, Q J Math (2010) 61 (3): 373-380.
Ulrike Tillmann studies the effect of the homomorphism $\Gamma_{g,1} \to \mathrm{Aut}(F_{2g})$ from the mapping class group of a surface of genus $g$ with one boudary, that sends a mapping class to its effect on the fundamental group of the surface. She also studies many variants of this. The main technical theorem is that
$$\mathbb{Z} \times B\Gamma_\infty^+ \to \mathbb{Z} \times B\mathrm{Aut}(F_\infty)^+$$
is a map of infinite loop spaces, that it is a split epimorphism at odd primes, and that at 2 there is a slightly more complicated but still understood behavior.
