CMS Made Simple Forums

I just took over some sites that are runing on old 1.6 version. Is there a chance/way, without immidaite upgrade to run them on php 5.6?

That'll be a hard one to answer, CMSMS 1.6 was released in 2009 and PHP 5.6 in 2014, so likely quite a lot changed in those 5 years. I think all you could do is try it, then deal with each error as it comes up. I imagine upgrading the CMS to at least 1.11.x would be easier than modifying the code manually to fix each issue though. It will also depend on which third-party modules are in use.