The downside to having the blog be on a separate domain is that your main site won't receive the direct benefit of the links, social shares etc that your content draws. While linking from the new blog might help pass some authority to the main site, I don't think it's as beneficial as having the content be on the main site.
But no, it shouldn't hurt anything. It just might not be worth the time when you could be continuing to add more content to your current blog instead of starting from scratch on a new one.
You'll have to decide if you think the benefit from having keyword optimized urls for your new articles is greater than the cost of the new content not benefitting the authority of the main site as much as it would if it was on the same domain (I hope that makes sense). Also, if your main site has any authority at all, your content on the current blog will probably rank higher than the same content would on a new blog. Optimized urls are not as weighty of a ranking factor as domain authority. So those are just a couple things to think about.
If you do decide to start the new separate blog, I'd avoid having lots of links going back and forth between the two domains. Keep them one-way, driving traffic and authority from the new blog to the main site.