Nope. All snapshot reports - whether you have a Pro subscription or not - are limited to tweets from the past week. This is a limitation from Twitter, and we can't get around it. 

However, if you're looking for in-depth, full coverage analysis of tweets posted more than one week ago, we can provide that through a custom historical analysis. This historical tweet analysis will include all tweets posted for your search terms from anytime in Twitter's history, whether it was last month, last year, or five years ago. This is a more comprehensive analytics offering than our one-time static snapshot reports, and a great option if you want in-depth analysis of older tweets. Request a quote here.