You can’t have more than one appsettings because that’s the name of a section. You can add a new section though that uses the same kind of section definition as appsettings. E.g.,
<configuration>
<configSections>
<section name="DatabaseConfig" type="System.Configuration.NameValueFileSectionHandler, System, Version=2.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089"/>
</configSections>
....
<DatabaseConfig>
<add key="Whatever" value="stuff"/>
</DatabaseConfig>
</configuration>