No, they are unable to grant you any further desires. According to practically all modern texts, genies can only grant the number of wishes that were initially given (often 3). Wishes for wishes are either invalid and squandered, or they are treated as if they were never sought. Either way, it is considered bad luck to try and pull off another miracle by wishing for one.
Genies have been a popular subject for stories throughout history, probably first arising out of the need for supernatural beings that exist only to serve people. They have been described as slaves who were freed by prophets or kings, and often taken back as an act of kindness. Some genies prefer not to be freed from their contract with someone, and will always find a way to escape. Others may feel that slavery is a fair deal and do not mind working for their freedom.
The concept of a genie in a bottle has existed for many years. A common story goes like this: A king has a beautiful daughter who is promised to the most powerful man in the world. Not wanting to risk being outdone by another kingdom, he puts a spell on his daughter's wine so that it will make her drink forever. The prince falls for her anyway, but she loves the free spirit inside every human being more than anything else. She breaks the spell by asking for a glass of water and finishes the wine herself. The king forbids her from ever drinking wine again, but she ignores him.
A genie can never give you too many free wishes. Or, to put it another way, I hope that each remaining desire could meet an endless number of requirements that may be individually asked and granted. Otherwise, what's the point?
The only limit to the number of requests a genie is willing to grant is its own discretion. It can't give away everything it grants in hopes that some future request will make it go back on its word.
A genie can only grant your requests if you ask for something reasonable. If you ask it to make yourself rich or powerful enough, there's no telling what might happen. The genie could decide to keep you as its servant or pet instead of freeing yourself.
The more wishes you make, the more likely it is that you'll run into problems later when trying to fulfill one of them. For example, if you ask the genie to make all of your dreams come true, then maybe you shouldn't also want it to kill your neighbor as well.
Genies are the magic of the Arabian Nights. They're fun and fascinating, but also dangerous and unreliable. You have to be careful how you use your power over them. At the same time, they're also very rewarding if you know how to handle them.
You may accomplish this in a variety of ways, including:
A better question, in my opinion, is why do genies grant three wishes? Because each wish reflects one of the three states of life: past, present, and future. The first want is to modify the current situation, sometimes known as the "Get me out of here!" request. The second wish is to create a new possibility, often for better or worse. The third wish is to avoid any possible future misfortunes.
Here are some examples of genie wishes from children's stories:
The first wish of the Genie in the Bottle was for a prince to come release him from his bottle. When this didn't happen, he made a second wish for money so he could buy food and clothes. He ended up spending all the money on alcohol which caused him to lose his mind and be locked away in a hospital where they could care for him.
In Arab mythology, Al-Jinn (the genie) has three main attributes: he can assume various physical forms; he can speak with humans if granted permission; and he can limit another person's freedom of movement by tying them up with chains. Al-Jinn has a list of requests that range from trivial (a single cup of water) to serious (release the prisoner). If the human denies any of his requests, the jinn will use his magic to destroy him.
Once a genie has granted its limit of wishes, it cannot grant wishes for a period of time (typically one year), and cosmic law states that the same genie may only grant its limit of wishes to a single creature once during the creature's lifetime. However, if the genie chooses to do so, it can grant each of its grants separately at any point during this one-year period.
So, yes, you can make more requests from your DM in D&D. The rules don't say anything about this, but it can be done with no problem. But as long as you're playing by the book, having fun, and not hurting anyone else on purpose, then you should have no problems.
Yes, it is right. Me: I want to be able to make as many wishes as I want! Genie: That is a violation of the regulations...