Is there a way to have a different unsubscribe footer for Sales Insight emails?

You can configure this in the Admin | Sales Insight section.  The help article Configure Unsubscribe Footers in Sales Insight Emails explains how to do this.

I know you can choose to show/not show the default unsubscribe footer, what I'm asking is if I can create a new one just for Sales Insight.

How would it differ from the ones you send via MLM?  Do you want to have one unsubscribe for MSI emails and a different unsubscribe for MLM emails? 

If you just want different text,I think  you can do this by changing the text / HTML for the unsubscribe link in in the Admin | Sales Insight section for the user the creates the Sales Insight emails.  However, that user can't create MLM emails or they will have the same text.

Hmm yeah, we just have the one user (myself) right now that creates both kinds of emails (MLM & MSI).

The reason for wanting a different footer is the sales insight emails are a bit more personal than most of our MLM emails (aside from nurturing emails, which I would also like to change the unsub footer for) so the text needs to be slightly different.

I've used other MA platforms that allow for this, so was curious how I would set that up in Marketo, but it sounds like it's not easily done.

Can you create another Marketo user for configuring the alternate unsubscribe text you want to use with Sales Insight emails?  You should be able to get your email administrator to set up other email addresses that deliver to you for this purpose.