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You'll get better results soliciting 10-20 links every evening before you go to bed. If you get one positive result out of forty emails, over time you can build up a more powerful website than by receiving a thousand links from eight domains.
Think of it like this:
Bottom line, there aren't any shortcuts to building a quality website that merits being at the top of the serps.
There are other important reasons why it's preferred to have many inbounds from unique websites, but that's outside of the scope of this thread, and there are a lot of threads to dig into in the Links forum that can give you a good idea.