Learn Italian: Avessimo comprato l'assicurazione due giorni fa! - If only we had bought the insurance two days ago!

This is an independent exclamative subjunctive. You can use the past perfect subjunctive (the congiuntivo trapassato) all by itself to express a deep regret about a missed opportunity in the past. It perfectly translates the English 'If only...' even without words like 'if' or 'only'.

Why use the past perfect subjunctive (Avessimo comprato) rather than the imperfect subjunctive (Comprassimo)?

We use the past perfect subjunctive because the missed opportunity happened in the past (due giorni fa). If you were wishing for something right now, you would use the imperfect subjunctive, like Comprassimo l'assicurazione oggi! (If only we were buying the insurance today!).

Are there words I can add to this structure to emphasize the regret?

Yes, Italians frequently add almeno (at least) right after the auxiliary verb in these standalone exclamations. For example, Avessimo almeno comprato l'assicurazione... translates to 'If only we had at least bought the insurance...'.

Can I still use se solo or magari with this specific sentence if I want to?

Absolutely. You could say Se solo avessimo comprato l'assicurazione due giorni fa! or Magari avessimo comprato l'assicurazione due giorni fa! to mean the exact same thing. Starting directly with the verb is just a slightly more dramatic and concise stylistic choice.