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

1. Starting Price: 4000 euros.
2. Condition: The coin is in condition 100 (MS), 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 2024, it was auctioned with a starting price of 5500 euros and sold for 5500 euros, with the same condition of 100.

4. Average Prices:
- Average starting price: 3666.67 euros.
- Average selling price: 4933.33 euros.

Given that the coin is in high condition and has had a recent selling price of 5500 euros, it is reasonable to consider that interest in this coin may have increased, especially if condition is a key factor for collectors.

Taking into account the starting price of 4000 euros and the average selling price of 4933.33 euros, as well as the highest selling price of 5500 euros in the most recent auction, an estimated maximum purchase price could be in the range of 5500 to 6000 euros, considering that collectors may be willing to pay a bit more for a coin in excellent condition.

Therefore, an estimated maximum purchase price could be 6000 euros.