The only thing that makes me think they might aim for 3 parts in total, is the fact that it didn't sell quite as highly as some might've hoped.
It'll definitely be regarded as a financial success on their part, and will probably end up similar sales figures as FFXV when all of the different versions are out (i.e around 9 million copies sold total). But a lot of us were thinking that such a legendary game in the collective imagination of the games industry would hopefully mean the Remake exploded in sales numbers, and become one of those games that gets into the tens of millions of sales (e.g Witcher 3, Skyrim, GTA, Red Dead 2).
That obviously hasn't happened. Whilst I'm sure they'll still be very happy with the sales numbers (especially given how many were digital, meaning they made more profit), it is kinda sad that the series hasn't increased its audience size at all in 25 years. If it WAS aiming for 20 million sales, rather than 10 million, I'd be much more convinced they were going for the 4 or 5 part story. But given that FFXV might end up outselling it in total numbers (even if it made less profit), Squenix might be thinking to themselves "we obviously shouldn't spend too much time on this when new entries are doing better"