There is a setting on Windows and Linux (but not Mac) called "Reuse instance", however it was unintentionally removed for some time and has been added again in v3.6, which is currently in beta. Before opting in to beta versions, please read this:
Settings - Spine User Guide: Beta versions
Unfortunately if you are using 3.5 you can't see the setting. You can try this though: close Spine, then open your prefs.json
file with a text editor:
Windows: <user home folder>\Spine\prefs.json
Mac: <user home folder>/Library/Application Support/Spine/prefs.json
Linux: <user home folder>/.spine/prefs.json
Inside the first curly brace, add reuseInstance:false,
, eg:
{reuseInstance:false,version:5,spineVersion: [snipped]
Now every time you start Spine, it should open a new window instead of reusing the existing Spine window.