Why would you want to keep your existing blog external, and start a new one on the site? Do you expect to get any benefit from having two separate blogs?
If the purpose of your existing blog is to promote your main site, then there would be no point in starting a second blog. You will be diluting your efforts, and - more importantly - confusing your visitors. It makes much more sense to continue to develop the existing one.
As for the more general question: should a blog be external (that is, with its own domain name) or part of the main site's domain? From an SEO point of view, it doesn't make any difference. The important thing is that the blog should contain interesting and fresh content that will attract visitors and encourage them to visit your main site, buy your products, or whatever else you are aiming to achieve.