As usual, the best answer is "it depends". Very OFTEN one can, but not always. A 2nd/3rd floor gets problematic unless you have a chase (like a chimney chase, for example) that you could use to route the cable upstairs, or you're OK with stapling new cable along the bottoms of the mopboards/baseboards and down the stairs. Under the edge of a carpet is ideal. If you have all "hard floors" and exposed cables are out of the question and you have no accessible chase, you're likely to have a hard time getting cables run across the gap between one floor's top plate and the next floor's sill plate. ANYONE is likely to have a hard time doing THAT, professional or amateur.
If you DO have carpeting, you can nearly always tug the veriest edge up with a pair of needlenose pliers, barely enough to tuck the cable under the edge. For stapling to mopboards/baseboards, you'll need a "cable stapler" built specifically for round cable, and you'll need some practice with it - if a cable staple penetrates the cable, it may cause you no end of grief. In either of these cases, you can certainly do the job yourself if you're comfortable with tools.
Have you tried running a two-antenna wireless router on each floor, with one antenna pointed straight up and the other horizontal? That may help.