The best way to start a SaaS based company and start gaining market share is through free-trials, testimonials and media coverage.
Have you got a free trial available at the moment? How have you been promoting it so far?
I'd be writing blog posts, sharing them out to related industries. Finding influencers and offering them trials in return for a review or a post (if they like the product).
It really comes down to getting users onto the product, and getting their experiences out there.
I'd love to jump on a call and walk you through these strategies and more if you're interested! It'll be easier to give you specifics when I know more about your particular business!