Last 2 months, about 20 per month.
Before that, I was averaging 1 a month.
What I did: cultivated a relationship with 3 infliencial bloggers in closely related niches.
Say my site was about dog training, I found bloggers in dog supplies, dog adoption, buying purebred puppies.
I became active on their sites via comments.
I developed content that would benefit them; basic infographics, basic videos, basic PDF white papers. I emailed them about them, they shared them via social media, I shared their shares. I shared other stuff of theirs. I engaged them via social media.
I used them on a round-up post.
They now share a post or 2 of mine a month, other sites then share my stuff because these influencers share my stuff. Most of the other sites have little traffic and don't mean much, but it all helps.
This took approx 8 months to build up this level of shares, and it kinda just ramped up out of no where.