So here's weird idea:
Einzbern family tries to create Grail, but just like in Canon fail.
That is until they meet a strange family called the Ainsworth.
Said Ainsworths are still from an alternate world, but have hit a snag in their own war, so through unknown means have travelled to this one and enlist the aid of their Alternates in the Einzbern family for the mutual benefit of both.
The two groups work together to create the grail, but meet the same problem as in the canon series (only one wish), so Grail war time bitches
However, due to the higher quality of their created grail (since both groups have been researching it for years), they are able to summon two sets of servants each. So two Riders, two Sabers, etc.
Also, The two families each make use of their own respective methods; this means we have the both the servants and the Class cards.
I'm still ironing out some fine details, but I'm thinking that in order to work around the fact that the Einzberns would still be missing some elements to even try and create a grail, they'll actually allow members from other families to marry into them (namely the Tohsaka and the Matou / Makiri).
So basically a Family Feud
between the two big bads of two different Fate stories