To estimate a maximum purchase price for the coin in question, let's consider several factors:

1. Current starting price: 5500 euros.
2. Coin condition: 100 (S/C), indicating it is in excellent condition.
3. Auction history:
- In 2016, the coin was auctioned with a starting price of 1500 euros and sold for 3800 euros.
- In 2023, the coin was auctioned with a starting price of 4000 euros, with an estimated price of 6000 euros, but it did not sell.

4. Average hammer price: 3800 euros, which is an important data point for understanding market value.

5. Auction trends: The coin has seen an increase in its starting price at recent auctions, suggesting growing interest.

Given that the condition is excellent and considering the current starting price of 5500 euros, which is higher than previous hammer prices, we could estimate that the maximum purchase price could be in a range above the starting price, but not too far from the average hammer price.

Taking all these factors into account, an estimated maximum purchase price could be between 6000 and 7000 euros, given the growing interest and the excellent condition of the coin. This would allow a buyer to be willing to pay a bit more than the starting price, but it would also reflect the risk that the coin may not sell at the expected price.