Can you link multiple sites to one Twitter account?

I have two websites that share a fairly similar topic, so I’d like both of them to use Tweetily to post to one Twitter account. Is this possible?

Currently one of the sites (Site A) can authorize with Twitter without any problems, but the other one can’t (Site B). I’ve tried authorizing them in different orders and the result is always the same: Site B no problems, Site A just returns to the Tweetily settings page without authorizing.

Any ideas?

https://www.ads-software.com/extend/plugins/tweetily-tweet-wordpress-posts-automatically/