Using AppleScript to Send Email from Mail.app to Multiple Addresses
I was able to tweak the set theAddress line and the tell msg to make new to recipient line to make the following code run as intended:

on run argv
    set theSubject to (item 1 of argv)
    set theAttachmentFile to (item 2 of argv)

    tell application "Mail"

        set theAddress to {"recipient1@domain.com","recipient2@domain.com"} 
        set theSignatureName to "Sig" -- the signature name 

        set msg to make new outgoing message with properties {subject:theSubject, visible:true}

        tell msg
            repeat with i from 1 to count theAddress
                make new to recipient at end of every to recipient with properties {address:item i of theAddress}
            end repeat
        end tell
        tell msg to make new attachment with properties {file name:theAttachmentFile as alias}

        set message signature of msg to signature theSignatureName

        send msg
    end tell
end run