If it's been a long time, your team likely enjoys your work because KCO HR goes very hard with the "no extension" policy for interns except when your team really wants you. You could speak to your partner about hiring prospects and possibility of being retained - if you don't ask, you will never know.
There's no "shame" in enquiring about the status of an "assessment" internship — and the one month policy is merely a codification of the intent that the firm only takes interns for direct assessment (even if you may be asked to extend your internship/come back again in the event that you have conflicting feedback and/or you're from a lesser known college which the firm does not have confidence on for having taught you well etc.)
As an associate, I've practically found that at least half of the interns come from "sources" and are neither competent nor interested. I cannot practically dedicate my time to evaluating such interns properly.
Thus, while your work will demonstrate your competence, a conversation where an intern tells the partner, buddies etc that they're looking for a PPO and want to be assessed to that yardstick certainly helps the team coordinate better to give you more opportunities and better evaluate your work. So, go ahead. Having this talk is highly, highly recommended.
As an associate, I've practically found that at least half of the interns come from "sources" and are neither competent nor interested. I cannot practically dedicate my time to evaluating such interns properly.
Thus, while your work will demonstrate your competence, a conversation where an intern tells the partner, buddies etc that they're looking for a PPO and want to be assessed to that yardstick certainly helps the team coordinate better to give you more opportunities and better evaluate your work. So, go ahead. Having this talk is highly, highly recommended.