Recently I was trying to build a multi-tenant application using Asp.Net Core. In that journey, I found an amazing series by Ben Foster where he wrote step by step guide to building multi-tenant application with Asp.Net Core and SaaSKit (A developer toolkit for building SaaS applications). With the help of that series, I am able to build foundation for multi-tenant application. I have added a bit more features in my sample like creating a database per tenant as they loaded the first time. I have shared my multi-tenant foundation application in GitHub so that other can get an idea to build their own. I will add more features along the way.
Hope this helps you to get started to build a multi-tenant application with Asp.Net Core. The code is available on GitHub.