In chapter 11 of the laws of kings (and their wars) (https://www.chabad.org/library/article_cdo/aid/1188356/jewish/Melachim-uMilchamot-Chapter-11.htm) the Rambam defines the basic obligation to believe in Moshiach etc. then he brings three proofs from the Torah Itself (5 books of Moshe) for the concept of Moshiach
Seemingly, the way the Rambam brings the sources seems to be extra, if he's only trying to bring a source that Moshiach is referenced in the 5 books, then why does he need to bring three proofs? Why not just one? Also, the way the Rambam words the proofs seems like he's trying to do more than only bring sources for the general idea of Moshiach, it seems like there are some deeper messages he's trying to say, the question is only what
For example, here is the section in question (beginning of Mishneh Torah hilchos melachim chapter 11)
In the future, the Messianic king will arise and renew the Davidic dynasty, restoring it to its initial sovereignty. He will build the Temple and gather the dispersed of Israel.
Then, in his days, the observance of all the statutes will return to their previous state. We will offer sacrifices, observe the Sabbatical and Jubilee years according to all their particulars as described by the Torah.
Anyone who does not believe in him or does not await his coming, denies not only the statements of the other prophets, but those of the Torah and Moses, our teacher. The Torah testified to his coming, as Deuteronomy 30:3-5 states:
God will bring back your captivity and have mercy upon you. He will again gather you from among the nations... Even if your Diaspora is at the ends of the heavens, God will gather you up from there... and bring you to the land....
These explicit words of the Torah include all the statements made by all the prophets.
Reference to Mashiach is also made in the portion of Bilaam who prophesies about two anointed kings: the first anointed king, David, who saved Israel from her oppressors; and the final anointed king who will arise from his descendants and save Israel in the end of days. That passage Numbers 24:17-18 relates:
'I see it, but not now' - This refers to David;
'I perceive it, but not in the near future;" - This refers to the Messianic king;
'A star shall go forth from Jacob' - This refers to David;
'and a staff shall arise in Israel' - This refers to the Messianic king;
'crushing all of Moab's princes' - This refers to David as II Samuel 8:2 relates: 'He smote Moab and measured them with a line;'
'decimating all of Seth's descendants' - This refers to the Messianic king about whom Zechariah 9:10 prophesies: 'He will rule from sea to sea.'
'Edom will be demolished' - This refers to David as II Samuel 8:6 states 'Edom became the servants of David;'
'Seir will be destroyed' - this refers to the Messianic king as Ovadiah 1:21 prophesies: 'Saviors will ascend Mount Zion to judge the mountain of Esau....'
א הַמֶּלֶךְ הַמָּשִׁיחַ עָתִיד לַעֲמֹד וּלְהַחְזִיר מַלכוּת דָּוִד לְיָשְׁנָהּ לַמֶּמְשָׁלָה הָרִאשׁוֹנָה. וּבוֹנֶה הַמִּקְדָּשׁ וּמְקַבֵּץ נִדְחֵי יִשְׂרָאֵל. וְחוֹזְרִין כָּל הַמִּשְׁפָּטִים בְּיָמָיו כְּשֶׁהָיוּ מִקֹּדֶם. מַקְרִיבִין קָרְבָּנוֹת. וְעוֹשִׂין שְׁמִטִּין וְיוֹבְלוֹת כְּכָל מִצְוָתָן הָאֲמוּרָה בַּתּוֹרָה. וְכָל מִי שֶׁאֵינוֹ מַאֲמִין בּוֹ. אוֹ מִי שֶׁאֵינוֹ מְחַכֶּה לְבִיאָתוֹ. לֹא בִּשְׁאָר נְבִיאִים בִּלְבַד הוּא כּוֹפֵר. אֶלָּא בַּתּוֹרָה וּבְמשֶׁה רַבֵּנוּ. שֶׁהֲרֵי הַתּוֹרָה הֵעִידָה עָלָיו שֶׁנֶּאֱמַר (דברים ל, ג) "וְשָׁב ה' אֱלֹהֶיךָ אֶת שְׁבוּתְךָ וְרִחֲמֶךָ וְשָׁב וְקִבֶּצְךָ" וְגוֹ' (דברים ל, ד) "אִם יִהְיֶה נִדַּחֲךָ בִּקְצֵה הַשָּׁמָיִם" וְגוֹ' (דברים ל, ה) "וֶהֱבִיאֲךָ ה'". וְאֵלּוּ הַדְּבָרִים הַמְפֹרָשִׁים בַּתּוֹרָה הֵם כּוֹלְלִים כָּל הַדְּבָרִים שֶׁנֶּאֶמְרוּ עַל יְדֵי כָּל הַנְּבִיאִים. אַף בְּפָרָשַׁת בִּלְעָם נֶאֱמַר וְשָׁם נִבֵּא בִּשְׁנֵי הַמְּשִׁיחִים. בַּמָּשִׁיחַ הָרִאשׁוֹן שֶׁהוּא דָּוִד שֶׁהוֹשִׁיעַ אֶת יִשְׂרָאֵל מִיַּד צָרֵיהֶם. וּבַמָּשִׁיחַ הָאַחֲרוֹן שֶׁעוֹמֵד מִבָּנָיו שֶׁמּוֹשִׁיעַ אֶת יִשְׂרָאֵל [בָּאַחֲרוֹנָה]. וְשָׁם הוּא אוֹמֵר (במדבר כד, יז) "אֶרְאֶנּוּ וְלֹא עַתָּה" זֶה דָּוִד. (במדבר כד, יז) "אֲשׁוּרֶנּוּ וְלֹא קָרוֹב" זֶה מֶלֶךְ הַמָּשִׁיחַ. (במדבר כד, יז) "דָּרַךְ כּוֹכָב מִיַּעֲקֹב" זֶה דָּוִד. (במדבר כד, יז) "וְקָם שֵׁבֶט מִיִּשְׂרָאֵל" זֶה מֶלֶךְ הַמָּשִׁיחַ. (במדבר כד, יז) "וּמָחַץ פַּאֲתֵי מוֹאָב" זֶה דָּוִד. וְכֵן הוּא אוֹמֵר (שמואל ב ח, ב) "וַיַּךְ אֶת מוֹאָב וַיְמַדְּדֵם בַּחֶבֶל" (במדבר כד, יז) "וְקַרְקַר כָּל בְּנֵי שֵׁת" זֶה הַמֶּלֶךְ הַמָּשִׁיחַ שֶׁנֶּאֱמַר בּוֹ (זכריה ט, י) "וּמָשְׁלוֹ מִיָּם עַד יָם". (במדבר כד, יח) "וְהָיָה אֱדוֹם יְרֵשָׁה" זֶה דָּוִד. שֶׁנֶּאֱמַר (שמואל ב ח, יד) "וַתְּהִי אֱדוֹם לְדָוִד לַעֲבָדִים" וְגוֹ'. (במדבר כד, יח) "וְהָיָה יְרֵשָׁה" וְגוֹ' זֶה הַמֶּלֶךְ הַמָּשִׁיחַ שֶׁנֶּאֱמַר (עובדיה א, כא) "וְעָלוּ מוֹשִׁעִים בְּהַר צִיּוֹן" וְגוֹ':
2 Similarly, with regard to the cities of refuge, Deuteronomy 19:8-9 states: 'When God will expand your borders... you must add three more cities.' This command was never fulfilled. Surely, God did not give this command in vain.
There is no need to cite proofs from the works of the prophets for all their books are filled with mention of this matter.
ב אַף בְּעָרֵי מִקְלָט הוּא אוֹמֵר (דברים יט, ח) "אִם יַרְחִיב ה' אֱלֹהֶיךָ אֶת גְּבֻלְךָ" (דברים יט, ט) "וְיָסַפְתָּ לְךָ עוֹד שָׁלֹשׁ עָרִים" וְגוֹ'. וּמֵעוֹלָם לֹא הָיָה דָּבָר זֶה. וְלֹא צִוָּה הַקָּדוֹשׁ בָּרוּךְ הוּא לְתֹהוּ. אֲבָל בְּדִבְרֵי הַנְּבִיאִים אֵין הַדָּבָר צָרִיךְ רְאָיָה שֶׁכָּל הַסְּפָרִים מְלֵאִים בְּדָבָר זֶה:
So first of all, as mentioned:
why does the Rambam bring three proofs, if he's only trying to find a source in the Torah for Moshiach to come and bring us out of exile, why doesn't the first proof suffice, which "includes all the statements made by all the prophets."?
he brings a total of three proofs, but the first two, from netzavim and bilaam, he groups together in the same halacha, together with the basic definition of Moshiach, but the cities of refuge proof from shoftim he puts in a new halacha. If he wanted to group them all together, why is the third one in a separate halacha? And maybe, if he wanted to put each proof in it's own halacha, then why are the first two grouped together?
why does the Rambam say the name of the parsha that the second proof is located in, "in the parsha of Bilaam...", while the other proofs don't mention the name of the parsha? (First one, merely a continuation of "The Torah testifies on him" (and not "in parshas netzavim it says...", like he said for Bilaam, and the third just "by the cities of refuge", which leads to::)
why in the third proof does he say "by the cities of refuge, it says...", the cities of refuge are mentioned multiple places in the Torah, masei, mishpatim, shoftim etc, so the term "by the cities of refuge", isn't a specific reference to any particular passage, the phrase on it's own (without the context) is ambiguous, in general the Rambam didn't give the exact name of the source for everything he says (like in the first proof where he says only "the Torah testified on him"), but if he would give a source, he should at least be specific about the parsha, like in the second proof where he said "in Bilaam it says...", why doesn't he simply say here by the third proof "in parshas shoftim it says..."?
regarding the second proof, if the Rambam only wanted to bring the basic idea of Moshiach from the parsha of Bilaam, he could have just said "in parshas Bilaam, he prophecized about Moshiach", and we would automatically know that it talks there about the "end of days" etc., why does the Rambam, first of all, say "there he propbecized regarding the two Moshiachim", including king David, and then continue to quote each verse side by side, comparing Moshiach and King David with every one? Why is the mention of David relevant to the laws of belief in Moshiach?
Based on the above 5 points, it seems that the Rambam is trying to do more than just bring a basic source in the 5 books for Moshiach, because if so, we wouldn't have the 5 difficulties mentioned above, so what is he trying to do, specifically, in the way he's presenting the 3 proofs?