Sorry if this has already been answered and explained, but I, too use Tapatalk from one of my tablets and yes, you absolutely can quote multiple posts at a time, tho, slightly different from the way CatFancier described(actually the Tapatalk format makes it even easier/simpler)
When you come upon a post that you would like to quote, but would still like to keep reading and possibly adding other posts so that you may reply to all of the posts at one time.. All you have to do is tap on the post you'd like to start with, the post will become highlighted, along with giving you the menu of several different options of what you'd like to do with the highlighted post(ie. Quote, Thanks, Share, Multi, etc)..
You'll want to tap on the "Multi" option which will automatically save that particular post allowing you to continue reading other posts.. If/when you come upon other posts that you would like to add you can simply click on the add button that you will see as an option once having initially started to collect multiple posts.. At any time when you are ready to, you simply click on the "Quote" option, instead of continuing to add more posts.. It will keep a tally of how many posts you have collected and once you tap on the "Quote" option it will then open you a new reply page with ALL OF THE MULTIPLE POSTS that you have clicked on and wish to reply to in one, single post..
Anyhow, sorry so long..hope that helps
**Please forgive the limitations that come w/my posting via mobile ATM**