In OTL ratification, the states that ratified by narrow majority were Massachusetts, nr. 6 on 6th of February, 1788, 187:168, New Hampshire, nr. 9 (the one that validated constitution) on 21st of June, 1788, 57:47, Virginia, nr. 10 on 25th of June, 1788, 89:79, New York, nr. 11 on 26th of July, 1788, 30:27 and Rhode Island, nr. 13 on 29th of May, 1790, 34:32.
It will not be hard to thwart ratification of Constitution by swaying 10 votes in Massachusetts.
So consider alternatives:
Constitution passed as per OTL, after ratification failed, the Articles of Confederation go on as usual;
Constitution passed as per OTL, after ratification failed, a new Convention meets to make a constitution of a rather looser union than OTL (though still different from Articles), and it gets ratified;
the original Convention proposes a Constitution of a rather looser union than OTL (though still different from Articles), and it gets ratified.
What could happen?