  We present a reflexive Banach space $\mathfrak{X}_{_{^\text{usm}}}$ which is
Hereditarily Indecomposable and satisfies the following properties. In every
subspace $Y$ of $\mathfrak{X}_{_{^\text{usm}}}$ there exists a weakly null
normalized sequence $\{y_n\}_n$, such that every subsymmetric sequence
$\{z_n\}_n$ is isomorphically generated as a spreading model of a subsequence
of $\{y_n\}_n$. Also, in every block subspace $Y$ of
$\mathfrak{X}_{_{^\text{usm}}}$ there exists a seminormalized block sequence
$\{z_n\}$ and
$T:\mathfrak{X}_{_{^\text{usm}}}\rightarrow\mathfrak{X}_{_{^\text{usm}}}$ an
isomorphism such that for every $n\in\mathbb{N}$ $T(z_{2n-1}) = z_{2n}$. Thus
the space is an example of an HI space which is not tight by range in a strong
sense.
