Steady Ricci solitons model Type II singularity formation under the Ricci flow. By utilising a procedure first introduced by Lai, we construct new one-parameter families of steady gradient Ricci solitons with positive curvature operator admitting $O(p)\times O(q)$ symmetry in dimension $p+q$, for any pair of integers $p,q$ at least $2$. If time permits, we shall discuss their geometry at infinity and highlight some open questions regarding their asymptotics.