If he's hurting you, then it's a problem. I never had an in-between like that. I only ever had rats who either nipped gently, to get my attention, or bit and tore my finger open. I used a kind of different approach to the one who bit me hard. I would get her out and hold her and pet her and generally love on her, in a really comfortable environment. When she would bite or try to, I would immediately make a yipping noise, set her away from me, and then put her in the time-out cage for a few minutes before we tried again. The time-out cage was not her normal cage. I didn't want her to think that going in her home was a punishment. Gradually, she understood that play time and snuggles ended when she hurt me. She stopped after three days. The important thing isn't so much establishing dominance, as it is reminding them that hurting you means the fun stops. This worked because she was very affectionate and loved our snuggle time, though. I don't know if the results would be the same with a more independent rat.
It's not so much alone time that will get to him, although he will get lonely, but it's that bond. Two or more bonded rats form a little family. They are a huge source of comfort and entertainment for one another. They sleep together and play together and the relationship with one another is very important. My first rat always seemed very happy alone, but the way she lit up once she had bonded with her cagemate was amazing. She became more social. She was bolder and more affectionate. She was in constant motion instead of sleeping all day. Trust me when I say, once the tricky process of intros are over and rats have grown to like each other, you will be so glad that you did it.
My mother was against me having a second rat, too. I was living at home when I first started keeping rats. There are a few ways I convinced her to let me get a second pet.
1. Show her that you are the primary caretaker of the rat. Let her see that you can take care of the rat's needs, therefore demonstrating that a second pet will not mean more work for her.
2. Let her bond with your current rat. Once my mom started to like my rat, it was very easy to convince her to let me get a second one. All I had to tell her was, "You know, General will be less healthy and more likely to be depressed alone," and she hated that thought.
3. Do some research and show her. Let her know that you are trying to take responsibility and be the best pet owner you can be, and with rats that means a cagemate. Show her that you've thought this through and you've done the research and show her that rats do better with a friend.
Pet stores aren't the only source of rats. Search rescues in your area, or look up ads looking for new homes for pets. Another male could be good, but also consider spayed females.