This is where you attempt to ride the coattail of influential people, companies, or websites in your niche. There is some SEO benefit, but the main goal is getting these people sharing with their audience, your write up thereby exposing your brand to them.
You obviously can't do it to a DIRECT competitor, but maybe an indirect one can help. You can write up something nice and fuzzy about their company, how to navigate their website, or highlight a unique selling proposition they offer OR something unique about their website - the purpose is just to stroke them. Implement that onto your website, and get your own social shares to it, then contact the company a week later and tell them about it. You can elude that they can share it with their family or friends, and followers, the more subtle, the better.
Most likely even if you don't elude it, they will want to stroke their own egos, and send it out to their Facebook fan page, get their employees to do the same, and send it out since it shows they've arrived. It helps if your website looks like a big brand and legit for this to work. They'll be sending you traffic all day and night, and may even backlink your article/content about them from their web properties. Each week do a write up for 20 different companies/websites and implement them onto your site. Then follow up. WORST case scenario they don't respond and you get the SEO benefits of ranking for "Company Review".
Example - Health Insurance Site: If I'm running a website about health insurance, I can do reviews on different types of other insurance like life insurance, mortgage insurance, OR even health related websites - vegan websites, Exercising websites, bodybuilding websites - all that encompasses health. Think about the average blogger that gets their regular healthy eating recipe blog reviewed by a "big brand" or "Mega brand" health insurance website. They'll think they've made it, and start pushing/promoting that one article you wrote on them. Since you aren't a direct competitor, they won't think twice.
Wouldn't people that want to eat healthier or lift weights want better health insurance? Isn't this your target audience? There is potential there. If you get really chummy with certain people, offer to let them join your affiliate program <- you see what I did there?
I'm just warming up... this isn't even my final form... We haven't even gotten to the dialectics...