There is a known halakhic principle of Tosefes Shabbos, that is one is supposed to accept or bring Shabbos a few minutes earlier.  One of the Lomdishe chakiros discussed is if this addendum to Shabbos is an early start for Shabbos, and essentially Shabbos itself, or is it a special zone to prepare for Shabbos, which is Shabbos-like in quality, but not actually Shabbos.

Our Gemara on Amud Aleph implies that a woman can marry on Shabbos and Yom Tov.  Tosafos here (“Demasar”) raises a question:

This contradicts what it teaches in Moed Kattan (8b) that we do not marry on Yom Tov, because we do not mix two semachos together.  That is, to celebrate both the joy of Yom Tov and the joy of a wedding at the same time would dilute either or both experiences.  (That is a lesson in and of itself regarding the concept of mindfulness and mitzvos.) Tosafos resolves the contradiction by suggesting when our Gemara discussed a situation of marriage on Yom Tov it was referring to the zone of Tosefes Shabbos and Yom Tov.  Presumably, Tosafos holds that Tosefes Yom Tov, while having the laws and restrictions of Yom Tov, does not have the Joy of Yom Tov, and thus does not involve a mixing of semachos forbidden by Gemara Moed Kattan.

We also see which side Tosafos holds in terms of the lomdus of tosefes Shabbos and Yom Tov, as he holds that it does not have the full kedusha, at least in terms of joy.

In the famous piyut, “Kol Mekadesh Shevi’i”, written by Rav Moshe Kloynymous, which also appears in Machzor Vitry, we sing:

דורשי ה', זרע אברהם אוהבו

God-seekers, progeny of Abraham his beloved

המאחרים לצאת מן השבת וממהרים לבוא

Who delay leaving the Sabbath, and hurry to enter it

There is a technical problem with this stanza.  Shouldn’t the chronological order be, “Who hurry to enter Shabbos” and then, “delay leaving it?”  Why does the poem begin with those who delay leaving Shabbos?  

I believe we see from here a proof to Tosafos’ side of the chakira.  Tosefes Shabbos does not have the full kedusha of Shabbos.  Therefore, the verse in the song follows the order of holiness, as we are discussing the praises of Israel’s devotion to Shabbos.  Those who delay leaving Shabbos are doing a greater mitzvah since the full holiness of Shabbos has already been initiated and remains until havdala. Then, also praiseworthy but secondary, are those who bring Shabbos in early, as according to Tosafos this addendum does not have the full holiness of Shabbos.

There is also a psychological reason to support this lomdishe idea about tosefes Shabbos.  Presumably the reason for tosefes Shabbos is to respect the human need for transition time.  This could be understood as similar to how Hashem gave Moshe time to ponder and reflect between each section of the Torah (see Rashi Vayikra 1:2.  Another lesson in and of itself in mindfulness!)  If so, how could tosefes Shabbos be a transition if it was fully Shabbos?  That would be like someone saying, “I need time to prepare for my upcoming marriage, so I'll get married a month earlier.”  If the person got married a month earlier that would not be a perpetration, instead, it would simply be getting married earlier!  It would only make sense if the person took on a transition period, such as an engagement period.  This is sensible way to understand the mitzvah of tosefes Shabbos.