There's nothing to stop an organisation running two, three or even four separate systems to document its approach to various standards. However imagine the amount of paperwork and potential confusion this can and will cause. Although we've yet to assist an organisation that has four systems we have worked with many that have two and lots that have three. The result of this approach has been to almost ensure that the systems have not been followed and that the documentation is there for the 'Assessors' benefit and not the organisations.
Most companies don't get into this situation by intent, they start with ISO9001 and somehow manage to separate this from the reality of running the business and find themselves with dusty folders that only Assessors see. Of course they have a system of sorts for managing health and safety (in reality in a lot of cases this is just a tired policy document) and it never occurs to them to use one to manage the other. Time marches on and someone mentions environmental management and before you know it there's a third system in place as ineffective as the first two.
Our experience in reviewing and remodelling these systems into effective management tools has proven invaluable to the organisations that have realised that just because their systems have evolved this way there's no reason not to intervene and start to create instead.