No matter how many raised beds you add, the amount of surface area does not change so that the amount of run off from rain water will not increase. So, unless you put in some automatic irrigation system you will not increase the existing issue of run off heading the "wrong way".
To level the beds on concrete, I suggest you create sub irrigation planters (SIPs). Basically you line the beds with heavy plastic or pond liner. You then put some sand down to protect the liner and then put a layer of a neutral filler with lots of gaps when packed ( something that doesn't alter its pH in contact with water eg broken bricks ) which is level, but say 6 inches deep at its lowest point. You drill an overflow point just below that, say 5 inches and put in an overflow pipe. This ensures that the raised bed water level does not reach the bottom of the dirt. You then lay down some type of root impermeable layer, eg weed mat, and create holes in it so that you can push some large net cups into which meet the bottom liner/sand. Fill those with potting mix. Then fill the whole raised bed with potting mix or similar artificial mix with easy drainage.
What happens now is that the water reservoir at the bottom can provide water for the whole bed by wicking up through the "feet" that you've poked through the weed mat by capillary action. And if there's a heavy rain, the water no longer perches above the weed mat, but drains into these legs and out the overflow hole.
You can google plans for a SIP planter.