I'm trying to find a framework which I can drop on top of bootstrap and add functionality to have elements which span more than one row (like you'd be able to do with a table). As far as I know, I can't do this with bootstrap directly (I can only make elements spanning multiple columns).
That's doable with bootstrap using nested rows/columns. There is no CSS framework I know of that implements it any other way, but it might be doable using display: table/table-cell/table-row/etc.