'experiences with various' is a correct and usable phrase in written English.
For example: "My time in college has given me many experiences with various people from different backgrounds."
Well before the term "crowdsourcing" arose, Consumer Reports supplemented its lab testing with surveys of subscribers, asking them to report on their experiences with various products.
Ramakrishna, as a direct result of his own spiritual experiences with various religious disciplines, including Christianity and Islam, fully endorsed the Hindu tenet that all religions are paths to the same goal.
Someone asked what I was working on, and I delivered my new spiel ("a cultural and intellectual history of anxiety, woven together and animated by my own experiences with anxiety"), talking about some of my experiences with various anti-anxiety and antidepressant medications.
Here's what Goop had to say: "Goop provides a forum for practitioners to present their views and experiences with various products like the Jade egg.
We reviewed experiences with various vaccination strategies using the currently available typhoid vaccines (injectable Vi polysaccharide vaccine [ViPS], oral Ty21a vaccine, and injectable typhoid conjugate vaccine [TCV]).
Instead, we describe our experiences with various types of valves – experience that was built up during many years of conducting Stark deceleration experiments – but we leave it up to the reader to value our conclusions.
In addition, from extensive experience with various types of valves, the GV produces beams with rather low peak intensity.
My hands-on experience with various computer systems and my interest in databases and programming came in handy with this work.
Samsung also said that in 2013, Smart Hub will offer a "more intuitive experience with various contents, live TV broadcasts, VOD, apps, Internet and such".
Despite evidence that many Australian adolescents have considerable experience with various drug types, little is known about the extent to which adolescents use multiple substances.
We estimated private landowner "conservation awareness" using a mail survey instrument to assess relative familiarity, knowledge, and experience with various conservation and land management options.
