You can upload your Tiffs into http://nextgis.com and get them back as TMS. But each raster will have separate URL. Also stacking on the fly is available (just list all raster styles in TMS url separate by commas).
Details: http://docs.nextgis.com/docs_ngcom/source/data_upload.html#raster-data
Here is an example of TMS URL: http://bushman.nextgis.com/api/component/render/tile?z=13&x=4784&y=2380&resource=36
Also you can create webmap like this: http://bushman.nextgis.com/resource/37/display