Let F be a torsion free sheaf of rank $n+4$ over $\mathbb{P}^1$ which fits in the SES
$0\longrightarrow\mathcal{O}_\mathbb{P^1}(-3)^{n+2}\longrightarrow F\longrightarrow\mathcal{O}_{\mathbb{P}^1}(-1)^2\longrightarrow0$
Is $F\simeq\mathcal{O}_{\mathbb{P}^1}(-3)^n\oplus\mathcal{O}_{\mathbb{P}^1}(-2)^4$?
The reason for this guess is the Koszul SES
$0\longrightarrow\mathcal{O}_{\mathbb{P}^1}(-3)\longrightarrow\mathcal{O}_{\mathbb{P}^1}(-2)^2\longrightarrow\mathcal{O}_{\mathbb{P}^1}(-1)\longrightarrow 0$