Yes—multiple 70D cameras can be connected over Wi‑Fi to the same network/computer, but setup matters. Give each camera a unique camera name and let each use automatic IP addressing unless your network requires manual settings. It’s also smart to set a separate download folder for each camera so files don’t mix.

Canon’s own workflow may be limited for controlling multiple cameras at once, but for transfer-only use, separate camera identities and folders are the key starting point. If direct multi-camera handling in EOS Utility still falls short, one workaround mentioned is sending images from each camera to Canon Image Gateway, then accessing them centrally.

For a more advanced solution, Canon’s EDSDK suggests that custom software can be written to communicate with multiple EOS cameras, and examples exist showing multi-camera handling. A heavy-duty workaround would be running separate virtual machines so each camera appears to its own instance of Canon’s software, though that’s not the simplest option.

So the short answer is: possible, yes—but the easiest practical path is careful per-camera Wi‑Fi setup, unique names, and unique destination folders.