MapUse.cs

public static class MapUseExtensions
{
    public static IApplicationBuilder MapUse(this IApplicationBuilder app, PathString pathMatch, Action<IApplicationBuilder> configuration)
    {
        if (pathMatch.HasValue && pathMatch.Value.EndsWith("/", StringComparison.Ordinal))
        {
            throw new ArgumentException("The path must not end with a '/'", nameof(pathMatch));
        }

        // create branch
        var branchBuilder = app.New();
        configuration(branchBuilder);

        return app.Use(next => new MapUseMiddleware(next, branchBuilder, pathMatch).Invoke);
    }
}

public class MapUseMiddleware
{
    private readonly RequestDelegate _next; 
    private readonly PathString _pathMatch;
    private readonly RequestDelegate _branch;

    public MapUseMiddleware(RequestDelegate next, IApplicationBuilder branchBuilder, PathString pathMatch)
    {
        _next = next;
        _pathMatch = pathMatch;

        // this is registered at the end of the pipeline
        branchBuilder.Use(subNext => { return ctx => next(ctx); });

        _branch = branchBuilder.Build();
    }

    public async Task Invoke(HttpContext context)
    {
        PathString path = context.Request.Path;
        PathString remainingPath;
        if (path.StartsWithSegments(_pathMatch, out remainingPath))
        {
            // Update the path
            PathString pathBase = context.Request.PathBase;
            context.Request.PathBase = pathBase + _pathMatch;
            context.Request.Path = remainingPath;

            await _branch(context);

            context.Request.PathBase = pathBase;
            context.Request.Path = path; 
        }
        else
        {
            await _next(context);
        }
    }
}