Obviously you can represent the values of multiple variables with text beside the marker. For example, on general aviation sectional maps, airport markers include text for the name, location identifier, control tower frequency, ATIS frequency, Unicom frequency, elevation, and runway length, among other information. For an electronic map, some or all text may be shown statically, on hover, on a click adjacent to the marker, or on a click in separate dedicated area of the display, depending on how often and critical the information is, and how much there is. If you have trained users that regularly use the app, you may be able to exclude the variables’ names to reduce clutter, relying instead on font and order of the values, format of the values, and a legend, to communicate what each variable is (e.g., elevation versus runway length).
Text representation is best when the user has already identified the marker of interest and wants more information on it. It’s also best when the user needs to read a precise quantitative value.
However, it seems you’re interested in data visualization with graphical representations of data. That is, your users will be looking for patterns in the data, the relation of certain markers to the geographic context, relative amounts across markers, and/or central tendencies, outliers, and trends over the geographic regions. The users may be searching for categories of markers or markers of certain approximate quantities.
A map marker has multiple graphic dimensions for representing a variable value, but which works best depends on the data type. These include (and are best for):
Shade (e.g., brightness of the marker): Quantitative data such as rates, intensities, and ratios.
Color saturation: Two or 3 levels of a quantitative variable.
Color hue: Qualitative differences, although there are some special cases or applications for indicating different levels of variable (e.g., green, yellow, red for levels of hazard).
Transparency: To indicate something not entirely there (e.g., under construction versus completed; temporary versus permanent).
Slant (e.g., the orientation of an isosceles triangle marker): Qualitative differences or a few levels of something, or quantities related to geographic orientation (e.g., wind direction).
Size: Quantities or levels, especially raw quantities (versus densities or rates).
Crispness (blurriness of the marker): To indicate two or three levels of uncertainty about the marker (e.g., inexact value of another variable).
Shape: Qualitative differences. If the shapes have pictorial associations with the quality (i.e., they’re icons), you can have quite a large number of shapes, although recognizable pictures tend to be larger and thus more cluttering.
Position (e.g., whether a graphic feature appears on top or below a marker): qualitative (categorical) or quantitative data (the most versatile dimension).
Density (i.e.,, how close graphic features, such as lines through your marker, are spaced): Quantitative data such as rates, intensities, and ratios.
Animation: For directing the user’s attention to particularly important markers. Characteristics of the animation (e.g., rate, smoothness of transition) can represent additional information. Provide users a means to turn off animation as part of your activation/deactivation feature.
A marker can be elaborated to use the same dimension multiple times. For example, the overall size of the marker can represent one variable, the thickness of its border can represent another, the size of a hole in the middle can represent a third, the size of a flag hanging off the side a forth, and the length of the “flag pole” a fifth. That’s five different variables represented by the size of something. The same graphic feature of a marker can also be used for different (but usually related) data by manipulating separate dimensions. For example, in addition to varying the length of the flag pole, you can vary its orientation to represent something else.
The need to activate and inactivate the display of certain variables requires special attention. The main concern is the user confusing a deactivated variable for a specific value of a variable if the user forgets (or is unaware) that the variable was deactivated. In some case this is easy. If you represent a variable with a flag pole, then removing the flag pole means the variable value is not displayed (…or it could mean the value is 0, depending the variable). If blue and yellow code a variable, then you can use a neutral color like gray when the variable is deactivated. Other cases are hard, such as for graphic dimensions “built into” the basic marker rather than added to it. For example if the size of marker represent a variable, how big do you make the markers when the variable is deactivated?
Presumably the purpose for deactivation is to reduce clutter. That makes sense for graphics and text that are added onto the marker (e.g., flags). For graphics built into the basic marker, you’re not reducing clutter much be deactivating them, so maybe it’s not worth the risk of confusion. It's a good idea to select a few high-use high-priority variables that are built into the base marker and cannot be deactivated.
The Learning Challenge
It’s pretty easy to come up with a marker symbology for representing 6 variables. Somewhat harder may be getting your user to understand the symbology. An easy-to-call-up legend is essential and tooltips are very helpful. Usability testing your symbology will help you arrive at the most intuitive markers feasible. Beyond that, you may need to consider training or tutorials for your users.
For more on graphic coding see my Putting the G into GUI. For issues in color coding, see my Breaking the Color Code (spoiler alert: color coding is sometimes more trouble than it's worth). Also consider getting an introductory textbook on cartography. For more advanced concepts, I can recommend Alan MacEachren’s How Maps Work.