Everything in this post is spoilers, so I'll be treating it as such. Don't look in the box below unless you played the first Senshinkan VN, Hachimyoujin.
The basic concept of the original Senshinkan was that individuals can, through a special mystic technique, go into a dream that forces them to experience innumerable versions of the past, present, and future in preparation for them to make a connection to the collective unconscious of humanity. Those who have done so gain the ability to manifest powers in reality that would normally be impossible, such as summoning and controlling demons and gods from the sea of humanity's collective unconscious. They can also grant a lesser version of their ability to their 'vassals', which lets them bring their own 'dreams' into reality.
The prime antagonist of the first game basically wanted to become the eternal antagonist of humanity, in order to keep us from rotting to the core, losing that which is best and worst about us. Yoshiya, the protagonist, wanted something similar, but his was directed to having others inherit the will of those who went before. Yoshiya's dream had him repeating the same period of time, focused on different antagonists, until he had faced all of them and was then forced to face the memories, emotions, and experiences of all those within his dream. This was part of the process of enlightenment (in the Buddhist sense) and eventually resulted in him facing off with Amakasu, the antagonist of the first game. In the final ending of the first game, he defeats Amakasu, and in the end he and his friends are reborn in 2015, one of the futures he 'saw' in his dream.
Bansenjin is based in this period, with the granddaughter of Don Karuma (a lesser antagonist from the first VN) arriving at the reborn (with no memories) Yoshiya's home, where he and his parents are living in relative peace. Since the prologue hits on the important points of why this is so in a vague way, I won't bother explaining.
That is a very vague summary of the basic outline of what went on in the first VN, and no one should play Bansenjin without having played Hachimyoujin.
Edit: At the same time, people who are used to Masada's style will have time getting into Bansenjin, simply because you have already experienced the majority of the characters in this VN. You know their root nature, you know their essential worries, their personalities, and how they will react. This is one of the reasons I hate sequels in VNs... but it is a lot worse with Masada, at least for me. I can see why he normally put two or three years between each release of VNs in a series (like five years between Paradise Lost and Dies Irae and three between Dies Irae and KKK) and why he made sure they shared as few obvious common points as possible, when it came to the characters.
To be blunt, Masada's skill when it comes to reusing characters without massive warping (ie KKK) is a bit... lacking. Not to mention Yoshiya isn't exactly the kind of protagonist you'd want to experience twice. His story was complete, so it really shocked me that they bothered with a sequel... and I'm just finding I can't enjoy it, despite the fact that there are some cool scenes already. There is just no sense of freshness for me... so I might or might not continue this, but it probably won't be for a little while.