Using two base addresses in Refit + cert x509

Question

Right now I am using the IHttpClientFactory interface and it works perfect. Now I need to use the Refit library. Is this possible to do?

i am doing this right now:

DI:

.AddHttpClient(
    "name_client",
    c =>
    {
        c.DefaultRequestHeaders.UserAgent.ParseAdd("Mozilla/5.0");
    }
)
.ConfigurePrimaryHttpMessageHandler(() =>
{
    // The web site needs login with certificate digital from path
    CookieContainer? cookieContainer = new();
    HttpClientHandler? handler =
        new() { CookieContainer = cookieContainer };
    handler.ClientCertificates.Add(
        DigitalCert.GetCert(context.Configuration)
    );
    return handler;
});

LOGIN:

public async Task Connect(string url)
{
    HttpClient httpclient = clientFactory.CreateClient(clientName);
    var res = await httpclient!.GetAsync(
        Path.Combine(
            string.Format(
                "https://serverlogin.com/cgi_AUT2000/CAutInicio.cgi?reference={0}",
                url // https://server2.com/
            )
        )
    );
}

GETDATA:

public async Task GetInfo(HttpRequestMessage message)
{
    message.RequestUri = new Uri("https://server2.com/cve_cgi/api/users/");
    HttpClient httpclient = clientFactory.CreateClient(clientName);
    HttpResponseMessage? res = await httpclient!.SendAsync(message);
}

I'm using refit like this:

DI:

services
    .AddRefitClient<IInterfaceRefit>()
    .ConfigureHttpClient(c =>
    {
        c.DefaultRequestHeaders.UserAgent.ParseAdd("Mozilla/5.0");
        c.BaseAddress = new Uri("https://serverlogin.com");
    })
    .ConfigurePrimaryHttpMessageHandler(() =>
    {        
        // get cert
    });

public interface IInterfaceRefit
 {
     [Get("/cgi_AUT2000/CAutInicio.cgi")]
     Task Connect(string reference);

     [Get("/cvc_cgi/dte/rf_reobtencion2_folios/")]
     Task<string> GetInfo(
         [Body(BodySerializationMethod.UrlEncoded)] Dictionary<string, object> data
     );   
 }

My problem with this approach is the change of base address. How could doing well? I have tried to change the base address in runtime with DelegatingHandler, but that approach doesn't work because the login was done to another endpoint.