The DropBox client, when installed, sends your MAC address to the DropBox server and it is stored in a database. Thus, if you try to install DropBox several times in order to get referrals, you will not succeed. One way to go would be to advertise your links using Google advertisements (has been done before), but that would require some initial investment.
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Get the referral link for the DropBox account you want to max out.
Open a browser within the virtual machine and use the referral link at the first step.
Download DropBox using the link from the previous step.
Create an account, you can use
mailinator or similar for the e-mail address (just to make sure since DropBox does not seem to send a confirmation e-mail).
Uninstall DropBox completely.
Change your MAC address to any randomly generated address, on OSX, that would be:
ifconfig en1 ether $(printf "%s:%s:%s:%s:%s:%s\n" `jot -r -w "%02x" 6 0 99`)
provided that en1 is the external WAN interface.
Jump to the third step and repeat (open a browser, use the referral link, download dropbox, create bogus account, uninstall dropbox, change MAC address).