Combine rows of a single file based on multiple matched columns, while retaining unique content by appending additional columns

I'm sure this code exists and I've read through a LOT of pandas / python documentation, in fact perhaps my answer is contained within Pandas, append column based on unique subset of column values but we can't seem to get it to work as below.

Using the example below, if both the Company and Place match, we want to combine the rest of the columns. IF there is unique data, then we would to retain the data in that column and append it as an additional column.

Here is the visual representation of what we need:

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