I always assumed colds ran on a 'no tagbacks' principle: once it's out of your system, it takes a while before you can get a cold again. Is there any truth to this, or can rhinoviruses hit you at any time?
The short answer is no, there is no minimum time between two colds. The reasons for this are different.
Mostly it has to do with the viruses which cause the common cold. There is a bunch of them causing what we call a cold, including rhinoviruses, coronacviruses, adenoviruses, human parainfluenza viruses, human respiratory syncytial virus, enteroviruses other than rhinoviruses and metapneumovirus. As much as 200 different virus serotypes are connected to this disease, alone 99 from the rhinoviridae. See the references 1-3 for more details.
Different serotypes means that two viruses of the same family (a rhinovirus for example) have different surface antigens on the virus and are not recognized by the same antibody. And this is what makes it difficult for the immune system. When it has learned to recognize and defeat one virus which causes a cold, it still has to learn how to do this with another (serotypically different) virus. So the adaptive immune system has to make highly specific antibodies every time it is faced with a new virus (which is of course not limited to cold viruses).
Once you have been infected with a virus and developed a sufficient immune reaction to develop antibodies, you are usually immune against this specific virus (with its specific serotype). Cold viruses live in communities, so when you move or travel, you will most likely encountered with different viruses, which your immune system doesn't know...
Finally there is another point which adds to the problem: Mutations of the viruses. The viruses are mutating constantly (RNA viruses at high rates) which changes their appearance and also their surface molecules (which are important for the recognition through the immune system). This leads to new serotypes, which are unknown to the immune system. See reference 4 for some more details.
If you are cured from the exact same virus, there is a less chance you will get it again.
As Chris already mentioned in the comment, one part of the problem, that different species causes similar symptoms which you know as cold.
Another part of the problem that the same species can have different subtypes and different antigens, so the immune system does not necessary recognize the same species with different surface antigens. The most well known from this group is influenza (flu) surface antigens e.g. H5N1.
Technically, I would say no. There is no period after a cold in which you can't get a cold again. This is because as mentioned in the comment, there are many species of rhinoviruses which all give very similar symptoms (not to mention mild flu viruses), to which the body will have no immune response.
However, it's important to remember how you get colds. It tends to be from people in your general area, and due to how colds spread this is all likely to be the same strain. Re-exposure to the strain that you have just recovered from would not cause the same infection again. It's also worth mentioning that the immune responses the body generates are in part non-specific (see innate immune system), and as such may help in preventing reinfection.
If you were to be exposed to a different species it is possible get a second cold after only just clearing the first one, but within real-life this is unlikely to occur.
Just like that while a cell is infected with a virus, other virus can not enter that cell As long as your body has not fully recovered and did not acquire full health so not be affected by another cold. The experience in cell culture and virus replication is observed exactly. This includes all viral infections. When the cell (as conceptual you'r body) were infected with virus A, B virus unable to replication in the cell's and enter the host cell, untill host cell recovery. The virus antigens that experss on the cell membrane prevents that other virus entering and until complete recovery those antigen is present in you'r cells membran's so cannot get a cold again, At least not the same cells infect