If a solution is super-saturated is it possible to add a substance to it without allowing it to crystallise? Does a change in temperature have to happen and reduce it's saturation if I want to add another substance?
It depends on what the solution is saturated with, the degree of supersaturation, and what substance you are adding.
If you are adding more of the substance with which the solution is supersaturated, the addition will likely provide a "seed" for nucleation (precipitation of the solid). The same will happen for the addition of many substances, particularly those that have similar bonding structure in the solid phase as the substance that is supersaturated.
As you suggest, adjusting the temperature will probably be necessary in order to further supersaturate the solution. If you just want to achieve a particular degree of supersaturation, you could just cool the solution by the necessary amount. This is assuming that the compound that is supersaturated has a solubility that decreases with decreasing temperature (most, but not all, compounds behave this way).
If you want to increase the solution's supersaturation at a given temperature, say room temperature, then you should heat the solution so that it is no longer supersaturated, then dissolve more of the compound, then let it cool back to room temperature. Of course it may precipitate during cooling depending on the degree of supersaturation and the conditions described above.
Yes, adding additional solute to a super saturated solution can be done without crystallization.
Adding additional solute to a super saturated solution and preventing crystallization is dependent on temperature, degree of agitation, and rate of solute addition. Changing the temperature is usually the easiest way to control the degree of super saturation, but you can experiment with the other variables as well. The degree to which these three variables affect any given system is dependent on the identity of the system and the amount of impurities (generally you do a lot of work to minimize impurities before you create a supersaturated solution).