A subscription can be created that generates a PDF to a folder.

The subscription be triggered by a stored procedure using the AddEvent SP in ReportServer with the subscription ID of the subscription.

EXEC ReportServer.dbo.AddEvent @EventType = 'TimedSubscription', @EventData = @SUBSCRIPTION_ID;

If the parameter needs to be updated, you can get the XML from the Subscriptions table and update it with .modify.

Here's an example of how it is used:

--GET SUBSCRIPTION PARAMTERS AND EXTENSIUONS
SELECT @EXTENSION_SETTINGS = ExtensionSettings, @PARAMETERS = [Parameters]
FROM ReportServer.dbo.Subscriptions
WHERE SubscriptionID = @SUBSCRIPTION_ID;

--LOOP SETUP USING ROW_NUM FROM QUERY - YOUR METHOD MAY DIFFER
SET @RECORD_ID = 1
SET @MAX_RECORD_ID = (SELECT MAX(RECORD_ID) FROM #RECORDS)

WHILE @RECORD_ID <= @MAX_RECORD_ID 
BEGIN

--SET EXTENSION OPTIONS FOR FILENAME AND PATH IF NECESSARY
SET @EXTENSION_SETTINGS.modify('replace value of (/ParameterValues/ParameterValue[Name="FILENAME"]/Value/text())[1] with sql:variable("@FILENAME")');
SET @EXTENSION_SETTINGS.modify('replace value of (/ParameterValues/ParameterValue[Name="PATH"]/Value/text())[1] with sql:variable("@PATH")');

--SET REPORT PARAMETER ID FROM VARIABLE @ID
SET @PARAMETERS.modify('replace value of (/ParameterValues/ParameterValue[Name="ID"]/Value/text())[1] with sql:variable("@ID")');

--UPDATE SUBSCRIPTION PARAMETERS 
UPDATE ReportServer.dbo.Subscriptions
SET ExtensionSettings = CAST(@EXTENSION_SETTINGS AS VARCHAR(8000)), 
    [Parameters]      = CAST(@PARAMETERS AS VARCHAR(8000))
WHERE SubscriptionID = @SUBSCRIPTION_ID

EXEC ReportServer.dbo.AddEvent @EventType = 'TimedSubscription', @EventData = @SUBSCRIPTION_ID;     --ADD SUBSCRIPTION TRIGGER EVENT 

--SET @RECORD_ID = @RECORD_ID + 1
END

There is one issue I found with your code.

When your code changes the parameter values and then execute the EXEC command, RS is queued that it has a report to run. This is done by the SubscriptionID of the RS report, and I do not believe that you can have more than one instance of the same SubscriptionID queued up at any one time.

The problem I found with your WHILE loop is that it will quickly process the next REPLACE parameter execution BEFORE RS has a chance to run the first EXEC with the first set of replaced parameters.

I used your code as a stepping stone to my final solution, that runs a single subscription over 20 times with different parameters and email address sets, but had to incorporate a hardcoded WAITFOR command after the EXEC to allow RS the time it needs to run the report before processing the next set of REPLACE statements.

But thanks for your post...It was a GREAT stepping stone.