Can we submit new TestFlight "pre-release" build while previous build is "In Review" (for beta review)? We submitted our app for beta review so that we can start using "External Testers" and go beyond the 25 person limit for Internal Testers. But while we are waiting for beta review to finish (currently "In Review") we need to keep testing internally and send out new builds. 

What doesn't work: While we were in review for one build, I tried changing the version to 1.0.1 (from 1.0) and updating the build #, and submitting a new build. That basically killed off the review process for the previous build and I had to re-submit for Beta Review for the new one.

Is there any solution?
No - you'll jam up the review if you don't let the first review complete once it is "In Review". Most of this is covered in the FAQ on iTunes Connect under Resources and Help.

The solution is to dig into the documentation (there's a video explaining the entire test flight process) and/or call Apple Developer support if you can't find the documentation on the web site.

I used to know where the link to support was on developer.apple.com, but Apple recently re-jiggered things on the developer web site and it's not where I expected. I suppose you need to log in to iTunes Connect and get help there on the contact us page.

The main solution I've discovered is to be patient and not try to game the system by submitting a second build if the first is taking a while.

If your build was "In Review" see if you can call and have them resume that review with the original build. Getting that first review is crucial for having subsequent reviews go faster as they can refer to their internal testing notes and just look over what changed, spot check things rather than do all the work for an initial build.