Can you run to perform a non-required mitzvah on Shabbos/Yom Tov?

Question

I have heard from many sources that running is prohibited on Shabbos unless one is running to do a mitzvah, i.e. toward shul for davening. However, could one run--on Shabbos or Yom Tov--to perform a mitzvah in which one is not strictly obligated? I am thinking of--possibly--running to maariv, or, for a woman, running to any positive mitzvah that is not required of her and for which she does not have a chazaka, such as davening in shul per se, or the second kiddush.

Related: Can You Run On Shabbos?

Answer 1

Rav Aharon Mazuz from Yeshivat Kisei Rachamim was asked the following question: Is the permission to run on Shabbos for a mitzvah relevant if there is a reason for it like trying to be one of the first ten in synagogue or is it alright to run for a mitzvah on Shabbos in all cases.

The Rav answers:

הרב המשיב: הרב אהרן מאזוז שליט"א. 1. עצם מה שאדם רץ לדבר מצוה יש בו מצוה ולכך רשאי לרוץ לדבר מצוה אף בשבת בכל אופן. וכמו שאמרו בגמרא ברכות (דף ו' עמוד ב') לעולם ירוץ אדם לדבר מצוה (כן גרסת הרי"ף) ואפילו בשבת שנאמר אחרי ה' ילכו כארי ישאג וגו

The very fact that a person runs for a mitzvah is in itself a mitzvah and therefore it is allowed to run for a mitzvah on Shabbos in every case as it says in the Gemara Berakhot 6b, “One should always run for a mitzvah (that's the text of the Rif) and even on Shabbos as the verse Hoshea 11 (10) says “They shall go (run?) after the Lord: He shall roar like a lion.”

So it seems that it is a mitzvah to run on Shabbos after any mitzvah.