This sounds like a problem caused by resource-heavy queries. If this is a trend, there are several solutions.
I would start by doing performance monitoring, in order to determine what exactly is causing the bottleneck. Is it CPU, RAM, or Disk IO.
Then, first try and see if you can optimize or rewrite the query so it consumes less resources. If that fails, and there is a hardware bottleneck, add more hardware. A final resort could always be to move one or more of the databases to a separate server.