Generally speaking, unless they have the separate vaccines for each disease (some companies have single product vaccines), they have a combo vaccine for the basics (Distemper, Parvo, Adenovirus, Influenza, Herpes with or without either Corona or Lepto). The lepto is given separately at times, and needs to be boosted yearly because it is a bacteria that has been deactivated, which tends to cause a less "dramatic" response in the immune system against it. Rabies is similar. The virus is so deadly that they give it in a killed variety so that the chances of it becoming a live virus (which the majority of your basic vaccines are modified live vaccines) are very rare. The body will not generally have a strong reaction to a dead bacteria, so they have to add in an adjuvent in order to get the body to respond and recognize the bacteria or virus as a bad foreign object. Lymes is caused by a bacteria, so it is also going to come generally in a killed form.
Each animal is a different creature. Some will have the ability to handle multiple pathogens at once (because let's be honest everyone, your body technically HAS to deal with multiple pathogens on a daily basis) and others may have an immune system that cannot handle it or get a more drastic response to it (allergic reactions). Vaccines have to go through testing just like anything else, so they have tested the multiple combinations and seen what kind of response they generally give at once. All vaccines are uniform in the dose size, so you have to look at your lifestyle and individual dog in order to decide what is best for it.
My dogs have always gotten multiple shots at once and I have not seen an allergic reaction in them. I work in vet clinics, so I -have- seen many different types of reactions to vaccines, but they are actually vastly less than they were a few years ago! The main reason for this is because they have been changing up the adjuvents used in the vaccines to make them safer, and get less of an overreaction by the body.
It is common for dogs to feel a little icky after getting vaccines because their bodies are responding to the foreign pathogen as it is supposed to. They generally are a little lethargic, possibly sore at the injection site and they could potentially have a low grade fever. It typically last just 24 hrs, but the soreness could be something that lasts a bit longer. Ever had a tetanus vaccine? I swear it took 3 days the last time for my muscle to stop aching like it was, and man did it ever hurt! So a mild "reaction" would always be expected.
A true anaphylactic reaction in a dog will have them vomiting within about 15-20 minutes of the vaccines being given. It is pretty rare to see that sort of reaction. The more common one is to see hives develop, their muzzle and around the eyes get swollen, start itching a good deal. It is more of a secondary allergic reaction, and if you had your pet vaccinated by a vet, they will treat allergic reactions for free and make a note in your pet's chart. The downfall with the multiple at the same time is that you cannot tell what caused it, however it is usually the killed vaccines that cause it and overall lepto has been the one that was considered the cause.
Truth is most clients don't want to have to come back for additional vaccines and complain as it is about pricing. :P So while it would bring in more revenue, the truth is that less people would be wanting to deal with that. The majority of people don't like having to visit their vet often lol.
And it wouldn't be really bad press for the vet if your pet had a really severe reaction and they passed. I've seen that happen ONCE out of all the years I've worked in the animal industry, and the two vets who were in the building had been in practice over 25 years and it was the first time they saw it either. It took all of us by surprise and we all felt terrible that it happened. The vet who was doing the appointment offered not to vaccination the other cat she had there (this is a client who we see many cats from and none had had reactions ever before) if she didn't want it and everything he did that day was free, including the cremation for the kitty who passed.
No vet wants to have something happen to your pet from routine preventative care. Just like no doctor wants you to have reactions to what they do either. I had an anaphylactic reaction to a vaccine as a child, but it was only the one, I got every other vaccine than that one, and even if its silly because no one is going to give me another MMR vaccine, I have an alert in my file and usually on me if I am in for a procedure of any kind.
But by all means, get involved with your pet's healthcare! Ask questions, figure out why they recommend things the way that they do, and if the vaccine is something that won't be an issue with your lifestyle, you can always say, I would not like that vaccine. We have plenty of clients who have said they do not want to do certain vaccines, and we respect that wish. Veterinary professionals really just want to see your pet happy, healthy and protected against harm.
It always makes us happy.