The short answer is that you can do whatever you want. 😉 The question, though, is whether you should. The answer is no. Here is why:

Occasionally customers ask how data from third-party sites such as Google My Business or Facebook Pages can be aggregated. I usually respond that this can be done by using custom field types. Since SNIP doesn’t provide built-in support for aggregating data from external sources, you would need to implement this yourself. This is often a challenging task—the APIs are typically complex and require substantial coding.

However, you may not need to go to that extent. Google’s review guidelines indicate that third-party aggregation of ratings is not allowed. The following excerpt is from Google’s guidelines as of May 2020:

If the review snippet is for a local business or organization, you must follow these additional guidelines:

• Sites must collect ratings information directly from users and not from other sites.

This differs for products. There are third-party tools that aggregate product ratings (such as Stamped.io), which you can use. But you should not use them for your business or local organization.