You say "we both finish a Masechta together". Do you mean "almost finish"? Doesn't the finishing happen at the siyum itself?

Yes, technically speaking (although practically speaking, and much to my chagrin, many people study the final part of the Masechta before the siyum...)

This could lead to a chaburah of 8 people holding 8 siyumim during the 9 days on the same piece of learning.

Are both celebrating Torah study? What's the problem? Are either just facades to ignore mourning the Temple and with no one caring about the Torah study? What's the heter?

although practically speaking, and much to my chagrin, many people study the final part of the Masechta before the siyum... From personal experience (a Siyum of my own group shortly (fortunately!) before the COVID-19 shutdown; and from experience with many others), I suspect the vast majority of people planning to lead a Siyum will study the last portion in advance to be prepared - I certainly did. They just might not study it together as a group in the usual way.

@manassehkatz when I teach the last section of a masechta to others who plan on making a separate formal siyum, I ask them to leave the room, and not to read that section (at the very least, not to read it out loud) until their siyum. Preparing the last section means that one is not actually finishing the Masechta at the siyum, and anyways, it would be nice for those at a siyum to see the shiur and/or Chavrusa go through their regular learning process.

@רבותמחשבות I think a lot depends on the specifics. If the Siyum is a big crowd (e.g., at tables at a Seudah, or seated in Shul) with one person getting up in front of everyone, then it won't be "see the Shiur and/or Chavrusa go through their regular learning process". But in any case, I wouldn't study that last Pasuk/Sugya in the regular group/Chavrusa. Just privately to be prepared.

Not reading aloud in advance seems ridiculous. What if the last sugya is very detailed and you spend two weeks on it? You can't say it out loud lest you lose your chance at a siyum? Clearly not. You're done when you decide you're done. If you prepare a dvar Torah today to give tomorrow and that's when you plan to be done thinking about that sugya, then you celebrate with a siyum tomorrow after giving it.