Share connections from a pool with different databases in the same PG server

When we are using TLS connections to a PG server the cost to keep opened multiple connections to different databases is high. So I'd like to implement database switching to share the connections from a pool with different databases.

pool = await asyncpg.create_pool(database='postgres')

async def handle(queries):
    """Handle incoming queries."""

    results = defaultdict(list)

    for dbname, dbqueries in queries.items():
        async with pool.acquire() as connection:

            connection.set_database(dbname)  # I want this !!!

            async with connection.transaction():
                for query in dbqueries:
                    result = await connection.execute(query)
                    results[dbname].append(result)

Is it feasible with asyncpg?

Review asyncpg's pool and connection entry points, then check PostgreSQL's connection and database semantics. The issue names no files or tests; done would require a maintainer-confirmed scope and a reproducible acceptance case for sharing pooled connections across databases.