Our Sages taught: The mitzvah of Chanukkah is a [single] candle for [each] person and their household; and for the mehadrin [scrupulous] a candle for each and every one; and for the mehadrin of the mehadrin: Beit Shammai says: The first day he lights eight, from here going [forward], he goes on reducing, and Beit Hillel says: The first day he lights one, from here going [forward], he goes on adding.
(א) כַּמָּה נֵרוֹת הוּא מַדְלִיק בַּחֲנֻכָּה. מִצְוָתָהּ שֶׁיִּהְיֶה כָּל בַּיִת וּבַיִת מַדְלִיק נֵר אֶחָד בֵּין שֶׁהָיוּ אַנְשֵׁי הַבַּיִת מְרֻבִּין בֵּין שֶׁלֹּא הָיָה בּוֹ אֶלָּא אָדָם אֶחָד. וְהַמְהַדֵּר אֶת הַמִּצְוָה מַדְלִיק נֵרוֹת כְּמִנְיַן אַנְשֵׁי הַבַּיִת נֵר לְכָל אֶחָד וְאֶחָד בֵּין אֲנָשִׁים בֵּין נָשִׁים. וְהַמְהַדֵּר יוֹתֵר עַל זֶה וְעוֹשֶׂה מִצְוָה מִן הַמֻּבְחָר מַדְלִיק נֵר לְכָל אֶחָד בַּלַּיְלָה הָרִאשׁוֹן וּמוֹסִיף וְהוֹלֵךְ בְּכָל לַיְלָה וְלַיְלָה נֵר אֶחָד:
(1) How many lights do you kindle on Chanukah? It is a commandment that one light be kindled in each and every house whether it be a household with many people or a house with a single person. One who is extra scrupulous one may kindle light according to the number of people in the household, a light for each and every person, whether they are men or women. One who is the most scrupulous and performs the mitzvah in the most choice manner kindles a light for each person on the first night and adds on following nights one light.
מִצְוַת נֵר חֲנֻכָּה מִצְוָה חֲבִיבָה הִיא עַד מְאֹד וְצָרִיךְ אָדָם לְהִזָּהֵר בָּהּ כְּדֵי לְהוֹדִיעַ הַנֵּס וּלְהוֹסִיף בְּשֶׁבַח הָאֵל וְהוֹדָיָה לוֹ עַל הַנִּסִּים שֶׁעָשָׂה לָנוּ. אֲפִלּוּ אֵין לוֹ מַה יֹּאכַל אֶלָּא מִן הַצְּדָקָה שׁוֹאֵל אוֹ מוֹכֵר כְּסוּתוֹ וְלוֹקֵחַ שֶׁמֶן וְנֵרוֹת וּמַדְלִיק:
The mitzvah of the Hanukkah candle is an extremely dear one. And one must be careful with it, to publicize the miracle and to increase the praise of God and the thanks to him for the miracles he has done for us. Even if one does not have anything to eat except from charity, he borrows, or he sells his clothes and gets oil and candles and lights.
The first of these two halachot in the Rambam's Mishne Torah (ie source #2) indicates that the added level of "mehadrin" is not required, but rather is optional. That is, one who wishes may add lights per the householders, but the mitzvah only fundamentally requires one light per household.
The second halacha (source #3) , with its use of the plural neirot - candles - seems to imply that one must pursue the mehadrin level of multiple candles. How may we reconcile this seeming contradiction?
Rav Soloveitchik, Har'rei Kedem 183
It seems to me that the answer is, mehadrin min hamehadrin is not an independent idea limited to Chanukah. Rather, it is those who are scrupulous to pursue the Mehadrin level for all mitzvot who must here strive for mehadrin min hamehadrin. Regular people only must light one candle, and it is only these "Mehadrin" folks who are required to light multiple. [In fact, there is an alternate text of Maimonides here which reads "mehader et hamitzvot" - one who strives to glorify all the mitzvot, rather than what we have in our text, mehader et hamitzva, indicating just this particular mitzva of Chanukah]. It is these scrupulous people who must sell their clothing, etc, in order to acquire multiple candles, for all the members of their household.
--> This notion, that people can change their personal status vis-a-vis the observance of certain mitzvot, can be seen in other areas of halacha as well. R. Soloveitchik draws our attention to one such example, as follows in the next source:
זֶה הַכְּלָל כָּל שֶׁאִלּוּ הָיְתָה שֶׁלּוֹ הָיָה טוֹעֵן וּפוֹרֵק הֲרֵי זֶה חַיָּב לִטְעֹן וְלִפְרֹק בְּשֶׁל חֲבֵרוֹ. וְאִם הָיָה חָסִיד וְעוֹשֶׂה לִפְנִים מִשּׁוּרַת הַדִּין אֲפִלּוּ הָיָה הַנָּשִׂיא הַגָּדוֹל וְרָאָה בֶּהֱמַת חֲבֵרוֹ רוֹבֶצֶת תַּחַת מַשָּׂאָה שֶׁל תֶּבֶן אוֹ קָנִים וְכַיּוֹצֵא בָּהֶן פּוֹרֵק וְטוֹעֵן עִמּוֹ:
The general rule is as follows: if your own animal were in need of loading and unloading [a heavy burden], and you were to do it for your animal, then you are obligated to do so in a similar situation for the animal of your peer. Those who are pious in this regard, and go above and beyond in these situations - even if one were the president - and one were to see another's animal buckling under its burden of straw or canes, etc., then they must help load and unload with the owner.