Expanding Observations and creating unique pairings

I currently have data that look like ( a much larger version) of the following:

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Here, ID is a person's identifier, X1 is variable 1 and X2 is variable 2. What I want is to expand this dataset and create unique pairings of individuals first. This means that for instance, individual 1 will be paired with individual 2 and 3 (2 data points) and 2 will be paired with 1 and 3 (2 datapoints) and 3 will be paired with 1 and 2 (2 datapoints). Thereafter, I wish to sum over the variables X1 for each individual with the individual that she is paired with. So for instance, this new variable X3, for the first 2 datapoints, will consist of a sum of the value of X1 for individual 1 with X2 of that of individual 2 (1st Data point) and the sum of the value of X1 for individual 1 with X2 of that of individaul 3 (2nd datapoint). This has to be done for all individuals in the dataset. I envision a dataset that looks like the following:



Any help is much appreciated!