Anyone got some nice ideas about ranged attacks beyond normal range (close range weapon to medium, medium range weapon to long...)?

Not sure what you're looking for exactly. There are a couple of weapons, such as the longbow, which allow you to fire them at one range increment more than standard with the addition of another challenge die. Other than that, there is the Extreme Shot action card which allows any weapon to be fired one range increment farther than normal by adding a Misfortune die and even that can be ignored if the Prepare maneuver is taken first. Other than that, you can't fire weapons beyond their listed max range. Or to look at it another way, the shot may extend into a further range band, but has no chance of hitting a target at a longer range than the one listed as the weapon's max. I'd be very hesitant to introduce any house rule that altered this since it would tend to negate the specialness of the longbow and Extreme Shot action.

I had the same thought, not to allow shooting beyond max range. But some of in my group will ask about shooting beyond max range and it is always good to here some other persons thoughts on the subject, before closing the door shut.

The designers already answered the question for you though, which I have referenced for you. The answer is yes, provided you take the Extreme Shot action or are using a weapon that specifically allows it. So, I'm not sure what other thoughts you need to hear. Now if you are just looking for suggestions for other ways to enable this or what other people may have done that have gone beyond the rules, perhaps you should repost the question in houserules subforum.

Also keep in mind, that max range is just that - weapons can only shoot so far. An arrow can't travel an unlimited distance no matter how good the archer is. Eventually gravity and trajectory surpass skill.