There are a lot of reasons that posts to this blog sometimes don't happen for months at a time, but one of them is that I can often get sucked down the rabbit hole that is Reddit. If you don't know about reddit yet, you may not want to click that link, but if you do know (and you're reading this blog), you may know about one of the communities (subreddits) there - a place called r/askscience. It's a forum where people can ask questions of a scientific nature (anything from "Why are pigeons so successful as an urban animal?" to "What's so special about the speed of light?"), and then actual scientists from a slough of different fields will answer. I'm a panelist (one of those scientists), in this community, and I've spent a lot of time answering questions there, so I thought I'd let that work do some double-duty here. I'll start with some questions that I answered a while ago, but I'll try to post future responses in a bit more timely matter. If you have any questions you'd like to ask, please do!
Question: Is it possible to get multiple different colds/flu viruses at the same time? If so, what are the effects?
Yes, this is called a "superinfection."
The effects will vary quite a bit depending on the details. Many of the responses of the immune system to an infection are general - if you get infected with two rhinoviruses (one of the virus types that causes "colds") of the same type or two rhinoviruses of different types, the cells around the area of infection will respond in essentially the same way - principally by activating inflammation and something called the "antiviral state."
The response of your adaptive immune system (T-cells and B-cells) will be a bit different, since there would be two sets of activating signals with a co-infection, but it's hard to max out an immune response, and to some extent the different viruses will be competing with each other. It's possible that it will take you longer to recover, but I'm not aware of any solid data on this.
On the other hand, if you are co-infected with two different types of infection, say a bacterial and a viral infection, this can cause serious problems, since the immune response necessary to deal with viruses and the response necessary to deal with bacteria can be quite different, and the response to one can be counterproductive to the response to the other. In fact, most people that die "of the flu" actually die from bacterial infections of the lung that were able to gain a foothold because of the immune response to the flu virus.
Follow-up question: Would having a fungal infection of say... of the skin decrease the effectiveness of the immune systems ability to fight a bacterial and or viral infection at the same time?
A fungal infection in the skin is not likely to effect the immune response in, say the lung. Again, it depends a lot on specifics, and some infections can have systemic consequences. But as I said before, it's hard to run out of immune response. The reason that having two different kinds of infections in the lungs is an issue is not because you're running out of immune response, but because the immune environment is different.
Think about it this way - say you're the military and you're trying to combat an invading army and also rescue hostages being held by terrorists. If the invasion is in Boston and the terrorists are in New York - no problem. You can bomb the army and send in SWAT for the terrorists. If the terrorists are in a building surrounded by the invading army, then getting SWAT into the building is going to be impossible, and bombing the army is going to kill your hostages. Different immune responses are necessary to combat different types of infections, and they're not always mutually compatible. But if the infections are in different places, the immune system is more than capable of local responses.