Yes you can be infected with two cold viruses at one time and if you do then you will usually feel much worse than having just one cold virus.
There are several different strains of the cold viruses around and you can be infected with cold viruses even more than once during the year and can have more than one strain of cold virus infecting you.
Some people only get 1 cold virus per year and some other people get 2 or 3 cold viruses per year and that can be normal as well.
Last year I got 3 different cold viruses and had them all through the year including summer, spring and fall and I went to the doctor and he said it was normal to catch 3 or even 4 different cold viruses during the year.
Sometimes there's more than one cold viruses going around through the year and you can catch a cold virus at anytime during the year and not just during the fall and winter months.
You're more likely to catch a cold or flu virus during the fall and winter months because most people are cooped up inside around other people during those times in a stuffy house with the heating on and the cold and flu virus usually lives in those areas more often and can spread more often as well.
Other times I've only caught 1 cold virus per year but other times I catch a few different cold viruses per year.
There's really no set amount of cold viruses that you can catch per year that is normal but normally most people don't catch more than a few cold viruses per year.
You might have a weakened immune system if you do catch more than 3 or 4 cold viruses per year but not always.