Is there a relationship between the properties of different charges of a fundamental particle? To begin with, I'm a high school student and so my understanding of QFT is quite basic. Due to this, I'd prefer a simple answer (it would be great if it's yes/no) along with a very basic explanation.
Essentially, I know that the three fundamental forces - electric, strong and weak force are results of spontaneous symmetry breaking. At low energies, the symmetry breaks and the forces "split".
My question is based on this. Now that the forces have "split" is there any direct relationship between these forces? For example, an electron has an electric charge of -1, a strong charge of 0, and a weak charge of -1/2. So is there a connection between the -1, the 0 and the -1/2? If one of the values was to change, would any of the other two values change? If yes, would it be both or would it just be one of them?
So in essence, could there exist a fundamental particle that for example has an electric charge of -2, a color charge and a weak charge of 1/2? I'm not sure if there is another restriction that doesn't allow the electric charge to go below -1, but ignoring these other restrictions, just based on the pure relationship between these charges, would changing one affect the other 2, and if it does then is there only a certain number of combinations of these 3 charges?
 A: The fundamental charges of the Standard Model are actually called "Weak Hypercharge", "Weak Isospin" and "Colour" (the first two "mixes" to produce the weak force and the electromagnetic force, while the third produces the strong force).  However, these 3 charges are independent from each other, in the sense that knowing one of those don't tell me about the other two.
More details (don't read the following if you are concerned about being confused): There are actually 2 different vertex factors for the weak force, corresponding to 2 different weakly interacting bosons (the W bosons and the Z boson).
A: Let me give you the view from the experiment side:
The model, called the standard model of particle physics, is a mathematical quantum field theory that fits the data up to now and  its predictions are continually   fulfilled.
In addition, the  integral and differential functions of the model have to obey a specific group theory, in order to fit the various measured charges in experiments, that lead to describing the fundamental particles and their composites, that you are asking about.

The local SU(3)×SU(2)×U(1) gauge symmetry is an internal symmetry that essentially defines the Standard Model. Roughly, the three factors of the gauge symmetry give rise to the three fundamental interactions.

Group theories are as strict as integration and differentiation, once decided upon, one cannot pick and choose the way the particles are represented, but the group theory imposes the specific way charges are combined that allow real particles and composites of particles to exist. One cannot pick and choose among the members of the group.
A good example is the prediction that a particle  called $Ω^-$ should exist, that was found experimentally and confirmed the quark model of the standard model.

The particle was found and confirmed the theoretical research that led to the development of  the standard model.
So it is not possible to arbitrarily  attach charges to particles, it is the standard model itself as it has developed that does the assignment, in order to agree with observations. If in future experiments observations bring more combinations of the charges that exist in the symmetries of the standard model, the model should change in order to agree with nature , and keep having predictive power.
