Changing Pagintation pages template

Hello,

I’m working on a site right now and I have a homepage hardcoded in using index.php with a loop of some recent posts.

At the bottom, I am using

<div>
<div><?php previous_posts_link('← Previous Post') ?></div>
<div><?php next_posts_link('Next Post →') ?></div>
</div>

for pagination. What I was wondering was how to make pages other then the index page (in other words https://www.mydomain.com/page/2, https://www.mydomain.com/page/3, etc.) look different then index.php. Is that at all possible? There is some featured things I would like to remove from the homepage. Unfortunately, I am developing this on a localhost so I can’t link to it, but I’d be happy to post more code here if that would help.

Thanks