If your mom wants a second dog, the general recommendation is different age, different size, different gender. But as Buzzu2 says, don't get it for the other dog. The things to be prepared for is that the two dogs become either do bonded that they don't listen to you, or that they hate each other and can't be in the same room.
When you say does that mean this would be a third dog in the house? Because the Mal would have to be taken into consideration too.
Oh and yes, sorry if it came out wrong, if we do get another dog their purpose is not for him, we also want another dog as well for companionship and to be another family dog, but one of the minor reasons is for our beagle (I want to put him into consideration as well because he is apart of our family) because he has a lot of energy to burst every day all day and I read that an another dog can help burst it with him while they burst their own.
And about the Mal, he only comes at least 3 times a year with our Uncle, he is very tolerant when it comes to our beagle so I'll think he will do just fine when he comes about. I wouldn't necessary say he is a third dog in the house, but we will definitely take that into consideration.
Also about the preparations if something goes wrong my mom already has that in the place:
We heard opposite-sex dogs do best together so if we do get a dog we are preferably looking for a female.
We want them to first meet in an neutral area ON a leash, If everything goes well we will introduce them being in the house together.
Jealousy is obviously a thing so equal amount of affection we be put inside both dogs to reassure our beagle he is not being forgotten.
The pups we will eat from different areas of the house because food is always a fight trigger.
If we get a shelter pup or a puppy, there will be one-on-one training sessions in an quiet room so they can focus.
Never leave them alone together,
Also crate them in different areas,
And everyday we will be training, we will introduce our dog to our newly introduced pup once he has adjusted and settled in, We don't want to cause any stressing for the puppy or dog.
If everything goes well, both will get a treat. When they get a treat they will associate our beagle with positive things.