I don't believe there's a way to do this now. You can submit a suggestion via the Feedback link at the bottom of most pages on LDS.org.
Depending on your goals, there may be some ideas to help you:
Online and LDS Tools
If you make any notes on the scriptures and/or bookmark them, you can go to the Notes and see what you did.
Note: They just released a substantially updated version of Notes on LDS.org. I haven't spent much time with it yet, but I'm guessing it still shows you things in chronological order of the most recent update.
Online Web Browser
You can open multiple tabs in your web browser. Depending on your browser's features and any extensions have have installed, you might be able to easily save open pages and have the browser reopen those tabs later.
LDS Tools
You can put scriptures in multiple tabs in LDS Tools. It remembers what you have open, so you can easily get back to them.