Thanks to True Alchemist for KR translated version of Volume 17's Preview
Spoiler for Gouki and Masaki :
Gouki did not object the engagement between Miyuki and Tatsuya not because because of his son.
As a member of 10MC, he thinks, Yotsuba wouldn't risk of losing magic talent through incestrous marriage for the future generation.
Based on my personal interpretation on Gouki's character, even if Masaki does not love Miyuki, he probably object the marriage.
After hearing everything Masaki replies that he is deeply in love with Miyuki and that it was love at first sight. Masaki admitted that he only got to dance with her once and Gouki replies that at least he shouldn't be hated by her
However, after witnessing his son's love for Miyuki, Gouki has two object, now.
Gouki is seven years younger than Koichi, but they are communicating as an equal because they are both leaders of clans under 10MC.
Inside of Gouki's mind, he was wondering why Koichi is helping him, but it was answered when Koichi states his intention to engage Mayumi and Tatsuya.
Gouki sees highly of Tatsuya because of Tatsuya's victory against his son. So, he strongly believes, incestrous marriage may risk of losing both Tatsuya and Miyuki's talents for the next generation. However, the chapter does not mention about the cooperation between Tatsuya and Masaki in Kyoto. So, he may not know Tatsuya being a part of the military.
Gouki managed to gain supports from Koichi, but he did not hand over the leading role to Koichi because he does not know what Koichi is upto.
Spoiler for Koichi and Saegusa sisters :
Saegusa Koichi has been doing background checks on Miyuki and Tatsuya. He knew about Miyuki's ability through 9SC and Yokohama incident.
He also knew about Cocytus; even though he does not know magic's property(its range and size of impact) and name, his researcher concluded that Cocytus is instant killing magic that has similar effect as Meteor Stream on anti personal level.
Regarding Tatsuya, Koichi found out, Tatsuya's decomposition, regrowth, and counter magic (gram demolition & gram dispersion) and he got a report that there is a high probability that Tatsuya was a S-class magician that caused Scorched Halloween.
He also know Tatsuya is close to 101 battalion that adopted flying magic at the battle field for the first time.
However, Koichi has no clue about Tatsuya being Silver. Koichi already suspected, Miyuki is a daughter of Miya even though he had no evidence.
Only thing, he did not know, was about Tatsuya being Maya's son.
Koichi worried about Tatsuya and Miyuki being in Yotsuba, but he had a confidence that one of them will leave Yotsuba, and he assumed, Tatsuya would be the one who will leave Yotsuba.
Koichi assumes, even if Tatsuya leaves Yotsuba, Tatsuya may sustain his connection with Yotsuba, but Koichi has a confidence that he can make Tatsuya to understand the importance of domestic power balance, however he was not thinking of the method. But, Koichi got outflanked by Maya.
The engagement is not something that other 10MC can interfere, so he was regretting not interfering it before it happens. But, Gouki's objection opens up a new possibility.
Koichi knows about his daughters especially about how Izumi gets seriously obsessed with Miyuki.("obsessed" may be a little strong, but I cannot think of a word that is a little weaker than obsession that fits in the sentence.)
Kazumi simplys says, she does not know Tatsuya much, and she only knows that he is talented in magic engineering.
Izumi's reaction and choice of words are very interesting. When she talks about Tatsuya, she uses very respectful words to describe him. It is similar to Hayama when he talks about Tatsuya to Mitsugu or Maya. Kasumi got shocked, and Mayumi opened her eye widely and turned to Izumi after they heard Izumi's words. Izumi talks about "stellar furnace", edited version of Phonon Maser and Invisible Bullet. But, she says, Tatsuya is somebody that she cannot comprehend because she feels like Tatsuya is looking at matters different from others. However, she cannot confirm whether he has a unique eye similar to Mayumi. Finally, Izumi says, Tatsuya is not somebody that she can handle. However, she loses herself and says, "If I have an ability to coquet / flirt with Tatsuya...... How can I let a man have Miyuki Senpai?" Even Koichi got concerned over Izumi.
Izumi objected because Masaki is a guy, so Tatsuya may not get mad, but if Mayumi proposed to Tatsuya, she assumes, Miyuki may get mad. And, Mayumi also claims about public's view on this matter because approaching recently engaged man may make Mayumi as a target for a bad rumor.
When Koichi asks Mayumi about Tatsuya, Koichi catches Mayumi's cheek turning red.
Mayumi basically declined by saying it's inappropriate for the women side of things to make these proposals, especially when Mayumi's the older one. Mayumi never said that she didn't like Tatsuya or hate him. She side stepped his attempt to ascertain her feelings.
Koichi tells Gouki that he still has to properly talk with Mayumi and as such he is not in a position to enforce her engagement with Tatsuya therefore he will support Ichijou's claim for the time being.
This spoiler mostly contributed from Flere821 Animesuki
Spoiler for Masaki and his father:
Masaki didn't even consider protesting against Miyuki's engagement, and he was browbeaten by Gouki insinuating Masaki is being a coward if they wait before protesting at this point.
Also, Gouki knows himself that he's in for a tough fight against the Yotsuba and welcomed Koichi's offer to introduce Gouki to others against Maya's declaration.
Spoiler for Koichi and Saegusa sisters :
Koichi considered the twins at the same time, before deciding they're not suited for Tatsuya. Both of them says "no" engaging to Tatsuya.
Izumi knew full well she's no match for Tatsuya. Though this was in the theories of 'hard core lesbian' and fearing Miyuki would be taken by other guys. She even thought it was a good thing that she can't be a match for Tatsuya, otherwise she'd have to marry Tatsuya and can't be with Miyuki. Izumi doesn't have that same reflexive 'cringe' of Miyuki being with a guy if it's with Tatsuya though.
Kasumi basically says she doesn't know Tatsuya well, though she had a knee-jerk reaction of "Mayumi's marrying someone? Hell No".
Koichi only noticed that while Mayumi disagreed about seducing Tatsuya away, especially since she is older. He knew things haven't been discussed with his daughters to the point he can just throw Mayumi at Tatsuya.
Koichi while talking with Gouki pretty much confirmed Mayumi and Itsuwa's arrangement fell through, both of them wants to turn their relationship back to 0. For Mayumi her prospects now is only Tatsuya or Juumonji.
Spoiler for Tatsuya and Miyuki :
If Tatsuya marriage Mayumi, Tatsuya will be in the Saegusa household. His name will be Saegusa Tatsuya.
Tatsuya and Miyuki should consider moving to Yotsuba side-house planned in Tokyo (as opposed to main residence/house) for the time being because of the marriage declaration.
Spoilers Plot on 2ch and content is added/changed after got verified by many translated reader at the forum
Yakumo got visitor from mysterious old man(Probably foreshadowing for the next volume?)
The following day they went to greet the Magic Battalion. All 101 members got promoted together. Fujibayashi is a lieutenant, Sanada and Yanagi are majors, Kazama is a lieutenant colonel and Saeki also got promoted but Tatsuya still a Special Lieutenant.
Tatsuya will continue with the Magic Battalion as the army and the Yotsuba are in agreement.
There is a scene where Kazama, Kyouko, and Tatsuya are talking about their monthly income. Based on the conversation, even though they got promoted, their income hasn't changed a lot, and it seems like Tatsuya makes a lot more money than regular soldiers because of magic engineer job. According to Mahouka BD vol.2, Tatsuya's monthly salary is 5 million Yen. (60 million Yen per year).
Kyouko used to have a fiance, but he died. Seems like, she still cannot forget her dead fiance.
In Shizuku's house, Honoka hears Tatsuya and Miyuki engagement news from Shizuku, Honoka cries. (Refer 4th Illustration)
When Honoka was given three choices: giving up, continuing to pursue Tatsuya, and becoming Tatsuya's mistress in the future, Honoka chose the second choice because she wants Tatsuya to interact with her and want herself (Honoka) to be the most loved by Tatsuya, so Honoka did not choose the first and the third option. Furthermore, Shizuku suggested the third option because Shizuku assumes, Yotsuba would allow Tatsuya to have many offsprings because of his extremely special magic talents.
Honoka's father is working for one of Numbers families, but the volume does not disclose which family Honoka's father is working for.
School starts, They are called to the principal's office and both the principal and vice-principal are waiting for them. It has to do with their school records. They ask them if they changed the information on them being siblings to cousins and engaged on purpose (I think the implication here is either hacking or falsifying information.).
Tatsuya says they should have recieved a letter of apology from his father and that it was never their intention to falsify information. The principal is still bothered by it but the vice-principal makes him see that it's possible. It can't be helped because information from those records (universal records) are public domain, so *a family* with *certain* interestest will try to protect that information.
The principal calms down and accepts Tatsuya and Miyui are not guilty, but that nonetheless it was necessary to straighten things up.
Then he also speaks about their engagement and the fact that they are no longer siblings. Within the school, their actions must be limited and proper. And with that last warning the meeting ends.
Erika and Leo are the same as usua