Declare multiple connection objects and multiple recordset objects.
E.g.:
Dim con1 As ADODB.Connection
Dim rs1 As ADODB.Recordset
Dim Cmd1 As New ADODB.Command
Dim con2 As ADODB.Connection
Dim rs2 As ADODB.Recordset
Dim Cmd2 As New ADODB.Command
For your sanity I suggest you use more meaningful names (e.g., "conCustomers", "cmdOrders")
Use similar code for each set of connections/queries.
Notes:
If there are multiple queries for the same connection, you can reuse the same connection, you' don't need a new one each time.
If the code is very similar for each query you could make the code more generic based on passed arguments and call it multiple times from a parent subroutine (code re-use).