Is that possible to make TLS 1.0 available to one particular app?

We are working on upgrading our web server to TLS 1.1 or later version only. For some reason, one of our web app (ASP.NET) can't connect to our smtp server after upgrading. I suspect the cause is MS Exchange server doesn't fully support transport on TLS 1.1 yet. So my question is that there is any possibility I can enable TLS 1.0 and 1.1, but make TLS 1.0 only available to particular application(s)? For some reason, third party framework/tools may not be our best choice. I am wondering if there is any built-in way can make this happen? Thank you, all.