We have in my team only used the statuses Open, Prepare, In progress, Test and Done in columns To Do, In progress, Test and Done. To make it more granular I'd like to have columns something like

and then create filters so each team basically only sees the relevant columns for them. So the Test team would see something like
To Do - UX - Code - Test To Do - Test In Progress - Done
as they wouldn't be interested in the different UX/Code statuses.
I assume we would need to create specific statuses for all 8 (or how many statuses we end up with) columns in the picture above to make it work, but I'm in a big organization with hundred of users in Jira. Is it possible to achieve this for our project only? In other words, could we ask the global Jira administrator in our organization to add the statuses we need to achieve this without it disturbing all the other projects that are currently running?
If it works i guess it could turn ugly if every project gets it's own statuses. To avoid that the plan is to ask the teams for suitable statuses and then talk to the global Jira administrator so we one set of statuses that would work for the whole organization even though we initially might be the only team to use them.