Change the template of multiple multisite pages at the same time

If these pages are using the default page.php template, just create a file called page-{slug}.php. So for example, if each subsite has a page with a slug of ‘my-cool-page’ you’ll create a template file called page-my-cool-page.php, upload it to the active theme, and all of the pages with that slug will automatically use that template. (If it’s not a custom-coded theme, be sure to use a child theme so your changes won’t be lost.)

If the pages are already using a custom template – i.e. you selected tpl-my-cool-template.php from the template dropdown in the editor – that will override `page-my-cool-page.php’ and you will have to update them one by one. But it does not sound like that is the case.