3TB? even on crap option like RDS up to 6TB is OK. You can get generic box with 200+ cores (actual cores not vCPUs) and 12TB of RAM from SuperMicro.
I supported a 20TB single-node DB, and it worked just fine. We had a lot of cold data though (about 10TB of it was solely for historical records, and 9.5TB of the rest was only accessed 4x yearly for massive reports).
The hardest part was never postgresql, mainly in numa related stuff.