I'm assuming the other sites don't belong to you as you have mentioned 3rd party.
As mentioned here, GA supports not using JavaScript itself to update your Analytics Reports. You can use the following parameters to place tracking pixel which tracks a variety of things. However, the most useful ones would be:
Parameter Description
utmac Google Analytics account ID
utmn Random ID to prevent the browser from caching the returned image
utmp Relative path of the page to be tracked
utmr Complete referral URL
conveniently provided on the Transaction Success page of your 3rd party website. The only problem is that the server-side of the 3rd party website must take care of the random ID generation required for the utmn
which prevents caching. (Generally images are cached, so they are not requested for again, but are retrieved from cache memory if the request is parsed again. This means if a user has already transacted once and he has it (the image) cached, if he transacts again, you will not be able to record the second completion because the request never triggers. To prevent this the random ID is generated so that the browser thinks it is not the same request every time.)
In utmp
, you can send /virtual/transaction/success or some other Virtual URL to be tracked. Take note, though, these pageviews and visits will appear in all your reports. But you will have the referrer URL so that it will help.
Another way would be to add this data obtained from the other websites as an Offline Custom Data Source in Universal Analytics.
Hope that helps!