Need more frequent sessions

I’ve been dealing with suicidal thoughts for probably 6 months now. I started therapy 3-4 months ago and it’s been helpful but the thoughts are still there. I would love to have twice weekly sessions but I already talked to my T about this and she said her supervisor thinks one is enough (she didn’t use this wording but she tried to make it sound like a good thing for me. “You’ll have more time for yourself and won’t have to worry about extra appointments” type of thing). It’s been a month since that conversation and I really think 2 sessions a week would be good for me. To the point where I’d be open to finding another therapist who would be willing to do this for me if she can’t. I’d be sad to leave my current T but this is really important to me. Should I ask again?

More than one session a week has been helpful to me. It doesn't sound like your T formally said "no"--so I'd try asking again and say it's something that you really want to try (and explain why). If it's a firm "no" for whatever reason, I think it's definitely worth looking into a T who offers what you want.

When I started therapy T said we'd do 1 Session a week for a year then up to 2 after If she felt that would be OK for me.
Looking back some 20 odd yrs ago now I didn't understand why the wait... NowI understand that a fragile mind needs time.