Yes, you can advance a muffed punt only in very limited circumstances, but generally not in the NFL or NCAA rules. Here’s a concise breakdown to clear up the common scenarios. Core answer

• In most standard cases, a muffed punt is a live ball only for possession purposes; the kicking team may recover it, but cannot advance it. If the receiving team muffed the punt (or fair catch is muffed), the ball is not advanceable by the kicking team and is ruled at the spot of recovery or downed where recovered. This is why a muffed punt recovered by the receiving team can be advanced by them, but not a muffed punt recovered by the kicking team. [Rule summaries and contemporary explanations align with this view, as discussed in recent rule discussions and game reports.]

Key clarifications

• What is a muffed punt? It occurs when a member of the receiving team touches the ball after it has been punted but before possessing it, or fails to secure possession in a manner that does not establish clear possession. The ball becomes live but cannot be advanced by the kicking team. The receiving team can gain possession and advance if they recover it after the muff. The official distinction is that possession has not been established for the kicking team to gain and advance the ball. [Rule references and explanations consistently describe muffed punts as not eligible for advancement by the kicking team.]
• What about a muffed punt with a fair catch? If a returner signals for a fair catch and then muffs the ball, the receiving team did not gain possession, so the ball cannot be advanced by the receiving team either; the ball is dead where recovered, and it becomes a turnover for the kicking team but cannot be advanced by the kicking team. [This nuance is highlighted in contemporary explanations of muffed fair catches.]
• Why can a muffed punt sometimes lead to a turnover? If the kicking team recovers a muffed punt, the kicking team gains possession, and the ball becomes dead at the spot of recovery or when the ball is blown dead, preventing further advancement on that play. [Rule interpretations and game analyses show this standard handling.]

Concrete examples to illustrate

• If the punt is muffed by a returner and the kicking team recovers the ball, the play ends at the spot of recovery; the kicking team has possession but cannot advance the ball on that play. A return by the kicking team on the same play to score a touchdown is not allowed under standard muffed punt rules. [Recent game analyses and rule discussions illustrate this outcome.]
• If the receiving team muffed the punt and then gains possession, they may advance the ball as a live ball, provided they possess it properly after gaining possession. The key is that possession was established by the receiving team. If the kicking team gains possession, they cannot advance the ball on that same play. [Rule explanations and comparative discussions confirm this distinction.]

If you’d like, I can tailor this to a specific league (NFL, NCAA) or a particular play you’re curious about, and I can pull the exact rule references for that scenario.