How can I increase the chance of receiving review requests? Is it appropriate to contact editors to offer my services as reviewer? I have a couple of published works, and I have received, so far, three review requests from three different journals. I have decided that reviewing service will help my resume at this stage. How can I increase my chance of receiving review requests from good journals? Is it appropriate to contact an editor and offer my service? Is it appropriate to contact the editors of the same journals that have already asked me to do review, and offer them that I would be willing to do more in future?
I think being a reviewer can round out your overall scholarly portfolio, but that is definitely not the big ticket item for a CV, especially if you are on or seeking a tenure track position.  If you are an early career investigator, focus on publishing high-quality articles, and then the request for reviews will start to flow.  You can reach out to editors and offer your services.  But, to be frank, I would invest your time in producing, rather than reviewing, scholarly works.