@Kate, At the start, this is not an issue for a caching plugin. You need to analyze the slowest queries in your network of sites and tune MySQL or your Themes / Plugins to make them more efficient and cacheable by your query cache in MySQL. From there you can look at W3TC to help you with caching your object caching using memcached for example, which will work very well reducing database calls on your site and not have the same saturation issues as APC does. Obviously W3TC's page caching will be a large help. Please write us if you have issues.
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