Two websites with semi-similar keywords on the same IP server / SEO that affect SERPS

Two websites have semi-similar keywords

  • 1 brand page / w keyword "Superman shoes"
  • and 1 retail site called shoes.com

Both run on the same server / hosting, same SSL certificate, similar design, same NS, similar DNS data and the same IP.

I understand from some blogs and rumors that this can confuse search engines like Google and Bing. The keyword "shoes" in this case does not specify the SERP that would be expected for both locations. (The reason why search engines do this is because some companies have tried to get both SERP 1, 2 and 3 entries with similar websites but different domains, but in this case this is legitimate.)

Now my question: What should be done to separate these two sites so they are treated as separate sites? (where it is not possible to change what they stand for or what they are)

One tip I got was to set up a separate IP for the two websites. But should I be more worried and organized if I make this "separation"?
(I can not change the server software and NS)

Thank you for your help / advice