How to run multiple SQL commands in a single SQL connection?

Just change the SqlCommand.CommandText instead of creating a new SqlCommand every time. There is no need to close and reopen the connection.

// Create the first command and execute
var command = new SqlCommand("<SQL Command>", myConnection);
var reader = command.ExecuteReader();

// Change the SQL Command and execute
command.CommandText = "<New SQL Command>";
command.ExecuteNonQuery();