Is there such a Parliament?
There's lots of them. The one that pops to mind best is Belgium; the 2019 general election returned a parliament that's heavily divided; the largest party has 25 seats with 76 needed for a majority:
||Bart De Wever
||Tom Van Grieken
||Elio Di Rupo
||Jean-Marc Nollet & Zakia Khattabi
A government has formed and fallen since then, but the incumbent government currently consists of a coalition of 7 different parties within Parliament:
Open Vld (Flemish)
So yeah, not so much bipartisan as...sept-partisan?
If so, am I right to think that it hinges on the Whips?
Eh, not so much. Whips exist to keep individual Members of Parliament in line and prevent them from deviating from Party policy. In cases like this, the far more major problem is for major coalition partners keeping the minor coalition partners in line and preventing them from deviating from coalition policy. So it's more a problem for the party leaders and their aides and so on, rather than the whips (who really only deal with members of their own party and at most the other party's whips).
Just want to address this:
On the other hand, the bipartisan system is always overburdened by ideological unlikeness within both parties.
This is not a burden, it is a feature.