Custom Sitecore Media Request handler to deal with media items with the same name but different extensions. If the media with matching extension is not found then the default Sitecore behaviour is used. This is directly inspired by the post by Martin Davies: http://sitecoreskills.blogspot.co.uk/2014/01/handling-duplicate-media-paths-in.html

MediaRequestHandler.cs

using System.Web;
using Sitecore.Diagnostics;
using Sitecore.Resources.Media;
using System;
using System.Linq;
using Sitecore.Data.Items;
using Sitecore.IO;

namespace MyProject.Custom.Media
{
    public class MediaRequestHandler : Sitecore.Resources.Media.MediaRequestHandler
    {
        protected override bool DoProcessRequest(HttpContext context, MediaRequest request,
            Sitecore.Resources.Media.Media media)
        {
            Assert.ArgumentNotNull((object) context, "context");
            Assert.ArgumentNotNull((object) request, "request");
            Assert.ArgumentNotNull((object) media, "media");

            string requestExtension = FileUtil.GetExtension(context.Request.FilePath);

            // if the extension does not match then try to find the alternate
            if (!string.Equals(media.Extension, requestExtension, StringComparison.InvariantCultureIgnoreCase))
            {
                // try to find a matching sibling of same name
                Item requestItem = media.MediaData.MediaItem;
                var alternateItem = requestItem.Database.SelectItems(requestItem.Paths.FullPath)
                                                        .FirstOrDefault(i => i["Extension"] == requestExtension);

                if (alternateItem != null)
                    media = MediaManager.GetMedia(alternateItem);
            }

            return base.DoProcessRequest(context, request, media);
        }
    }
}