We currently support 9.4.x,
would like to support 9.5.x, or 9.6 (RDS supports it https://aws.amazon.com/about-aws/whats-new/2016/11/amazon-rds-now-supports-postgresql-9-6-1/), and beyond, however the driver has changed somewhat:
Where before we used:
update the main services to use the new JDBC driver
test that the new driver can work with the currently included postgresql docker server container
upgrade and test the included postgresql docker server container to use Postgresql 9.6.