Some of the Big 4 firms allow you to reapply after 6 months from when you were notified of a rejection in your application. Rejections in your application mostly are due to a failure at the online testing stage.
Well lets be clear what we are talking about here, say you applied and failed once at one/all of the Big 4 firms, say either in Consulting or Accountancy. You then have 6 months from your rejection email date to apply again for most of these firms. So the strategy is always to apply very early on, do all the tests and if you fail you can then apply again. From what we have seen the Big 4 have don't really have a very large testing bank of questions although they test across a larger subject area.
The candidate feedback if you fail will tell you which areas you will need to focus on if you applied again. So in theory you have a slight advantage as you already know the process and if you're lucky similar questions will come up again. The tests would be similar across consulting and accountancy within the same firm. Depending on the date when you are allowed to reapply again look online for which departments and geographical areas are still hiring and submit your applications for those areas.
This is if you really really want to work in a Big 4 firm.