All wireless routers put out the maximum allowed power. It varies from country to country.
The key reason you are having trouble is the antenna are designed to transmit the signal horizontally. If you have external antenna on your router the easiest solution is to tilt one of them parallel to the table. If you do not have external antenna you can try to tip the unit on its side and see if it makes a difference.
If this does not work the only other choice you will have is buy a directional antenna which concentrates the power into a narrower beam. You of course need a router you can change the antenna on to even try this.
Floors are much more dense than interior walls so you will get much more signal loss. You can most likely improve your signal a little but there is no way to ensure it works. Sounds like you are in a multi tenant building and the floors and ceilings are sealed and insulated much better than a normal home. The features they use to attempt to block sound transmission do a great job of blocking wireless also.
The only sure way that will work is to run a cable. Depending who owns the building etc etc you may find a place you can run a ethernet cable. After that you have many options as to what to hook to the cable.
We live on floors 1&2 of a building, and are looking to share wifi internet with our neighbour directly above us on the 4th floor.
Most of the time the signal on the 1st floor is good enough for email - or for posting to this forum for example. Sometimes it cuts out or is simply too weak.
It's impossible to search online stores via the strength these things kick out.
Any suggestions on a good, reliable, powerful AP that we can hook up on the 4th floor and get decent internet on the 1st?
(Preferably suggestions from people using an AP for a similar application.)
Thanks in advance.