You can use twitter search page to bypass 3,200 limit. However you have to scroll down many times in the search results page. For example, I searched tweets from @beyinsiz_adam. This is the link of search results: https://twitter.com/search?q=from%3Abeyinsiz_adam&src=typd&f=realtime
Now in order to scroll down many times, you can use the following javascript code.
var myVar=setInterval(function(){myTimer()},1000);
function myTimer() {
window.scrollTo(0,document.body.scrollHeight);
}
Just run it in the FireBug console. And wait some time to load all tweets.