The simplest answer is not to make a second connection, but simply to change the default scheme after determining the name that this user needs.
For example, enter the secondary db name for this user:
$db = Zend_Db::factory(...options...);
$secondary_db = $db->query("SELECT secondary_db
FROM user_data WHERE user = ?", $userid)
->fetchOne();
Then run the query to change the schema. Please note that the statement USEdoes not support the prepared statement, so you need to execute it using the driver API:
$db->getConnection()->query("use $secondary_db");
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