Within SSRS itself this will be somewhat complex. I can see this being done a couple of ways, you could create multiple prompts, where they could enter a set number of customer numbers, say perhaps 10. Make the first one mandatory, the rest optional.
The second way, would be to use a string and let them enter a comma delimited list. You'd need to parse the list in your query.
Probably the best way particularly if you already have a custom front end for your reporting solution, is to capture all of the customer numbers in the custom front end allowing the application to have the user verify that customer 1 was john smith instead of customer 2 who was jane smith. Then you could pass that as a delimited string to SSRS, parse it in your query and you'd be all set.
-Luke.