I’m assuming you’re talking about iOS, which is how I use Ulysses too. On Mac, you can open multiple windows, and this is something they’re working on adding to iOS I believe.
The only option is to paste your research into the attachments field.
It is a slight problem not having access to multiple sheets, but pasting into the attachments has its benefits. It allows you to refer to more than one source of research, and use photo files from a number of sources, rather than just one.
The alternative is to use Scrivener, which allows you to quick reference another document while writing in the main editor. However, the drawback with this is that you can only reference one document. By pasting into the attachments field in Ulysses, you have access to more options.
The ideal solution would be to allow us to open up multiple versions of the same app. Have Ulysses open twice in split view, with a third version of the app floating.