From what I've heard, the amount of pile-up ATLAS and CMS can handle is limited by the CPU time it takes to reconstruct events, which can be alleviated by throwing more resources at it, but it is much better to develop quicker reconstruction algorithms.

Towards the end of last year, they had to start levelling the instantaneous luminosity to 75% of what they could achieve,† primarily to reduce the load on the grid.

† Edit: the maximum peak luminosity is still 200% of the design value, so the performance is beyond initial expectations.