From The TimeSplitters Wiki

TimeSplitters: Future Perfect was the first TS playable online. You can play a variety of modes online, and there are many clans that regularly play TimeSplitters online.

There is also a way to play TimeSplitters 2 online. It is explained at the TS2 Online Project Site.

The original author of Network does not have any further information on this article. The author may return to finish the article when information has been gathered, however they welcome anyone to expand on this article.