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Teresa,
You want to consider the cumulative impact, but that is not as simple as adding up the impact of each point where the risk could turn into an issue. That will overexaggerate the likely impact. What you are dealing with instead is a statistics problem that sometimes it will occur while at others it will not, and the impact will not always be the same. As an analogy, consider a simple variance problem where you have a series of items each lined up end to end with some variance in length (+ or  X) and you are asked to find the total variance. If you just add up the maximum variance for each length, you will find the worst case scenario which is extremely unlikely. Some items will be long and others short so the root mean squares (RMS) method is used to find a more realistic answer. In cumulative risk analysis, you have the same problem. Everything will not go wrong all the time. With the probability and likely impact of each event, you can find a mean (average) and a distribution. That's beyond my skill these days. If I was asked to do it myself, I would probably combine PERT estimation with RMS. Optimistic is zero for each occurance. Pessimistic is worst case. Most likely is somewhere in the middle. Find that for each item, find the sum of the squares, and take the square root. That isn't perfect by far, but it's more reasonable that everything goes completely wrong at every opportunity (although my job feels like that's the norm some days.)
Teresa,
Keith pointed several valid alternatives , you are dealing in this case with likelihood, frequency and impact, in this situation to make a exact calculation you will need a polinomial or poisson or a discrete distribution depending of the type of risk analisys. You do not know what is the frequency of a archaeological finding, you could research by previous situations occured in that area and use analogy nevertheless you also could simplify the situation. Mathematically it is easy to calculate the probability of successive independent events P (A) * P (B) , if you think that the probability is 70% of A, the probability of A and B happening sequentially is 49%, every time you add one more independent event the probability decrease P(A)*P(B)*P(C), but the funny thing is that the impact becomes more severe, so you should find a balance between the probability of findings and the impact. You could enter in deep statistical calculations and complicate your quantitative risk analisys , there are several samples in the net using Risk level = Likelihood * Impact * Frequency. Otherwise in this case you could make a separeted matrix that could address only this risk is not elegant or perfect but addresses the problem using the likelihood of one, two , three, four, five findings attributing the respective impact, two have a more clear insight of the situation. I'm not a statiscal expert so someone in the community could give a more accurate advice. Alexandre
Teresa 
A lot has to do with how dependent or independent the separate realization of the same risk event might be. For example, with the current COVID19 situation, if one team member is tested positive and is unable to work, this might actually increase the likelihood in the near term that others will also be tested positive and be unable to work.Hence the risk of team member unavailability due to contracting the virus is not an independent risk event, and potentially some sort of a compounding calculation may be needed to account for the progressive increase in the probability of occurrence. A similar one is the risk of severe reaction due to an allergy such as tree nuts or peanuts. The first time someone has the reaction, it may be mild, but with subsequent reactions it gets progressively more severe, hence the probability of severe reaction increases the more times the risk has been realized. Kiron Kiron
If you identify a risk you must to associate an action to the risk. The only way a risk occurs multiple times is if you "accept" the risk where the action is what you will do when the risk happend (for example executing a workaround). In other cases the actions are about the risk does not occurs multiple times. On the other said if you have a 70% of pobability of occurence then you are in the field of certainty which does mean it almost will occur indeed.
My first response and simplest option would be to consider it one risk event with a higher probability of it occurring.
This may not be appropriate if each potential risk event has different impacts and mitigation measures in which case the events should be considered separately. Some risk management plans, and registers, have subcategories. Using your example: Archaeological: a) south excavation (aboriginal claims) b) west excavation (grave yard) c) trenches (rumors of early encampment) I don't think there is one answer here. You have to consider what works best to manage project risks. 
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