about:config but this works only for opening new tabs using mouse middle button.
You could try Tab Mix Plus, an add-on I've been using since forever-ish.
Once installed, in the Tab Mix Plus options, Events -> New Tabs -> "Open new tabs next to current one". The option below it, "Open other tabs next to current one", doesn't do exactly what you're looking for.
Here is a relevant bug report:
Here are some more suggested extensions:
Personally I'm using the second one.
I'm using the Tab Control addon for the similar reason.
There is a setting: Position new tabs to right of current tab.