(edit: I’m leaving all the mistaken assumptions in just in case someone else makes the same mistakes)
I have an ancient Typo3 3.8.1 site on a remote server. I don’t have access to that server, and the team in charge of maintaining the site doesn’t know who to contact to get access to the server. I do have the admin rights on that site, though. (edit: no I don’t. oops.)
This is what I see in the (not) admin menu:

I’m not sure if this version supports extensions, I can’t find an extension manager anywhere. (because I’m not an admin)
I want to export the site so I can host it on a server on my own domain instead. The problem is the export file is too large, I can’t download it. Will I destroy the directory structure if I export a bunch of pages at a time?
Sometimes the server allows more memory and execution_time that the T3D Export. So, if you can change PHP files on that server, try to change typo3/sysext/impexp/class.tx_impexp.php – search for ini_set and change that settings. If the server allows, you can then create bigger t3d-files.
And you could try some shell-extensions to get hands on that server:
But to answer your initial question: you can crate a couple of T3D-files and import them again. Just force uid if you import them – and install all needed extensions first!