To estimate a maximum purchase price for the coin in question, we will consider several factors based on the provided data:

1. Current starting price: 1500 euros.
2. Auction history: The coin has been auctioned 16 times and has sold on all occasions, indicating consistent demand.
3. Average starting and hammer price: The average starting price is 433.85 euros and the average hammer price is 595.69 euros. This suggests that, in general, coins of this reference tend to sell for below the current starting price.
4. Previous prices: The hammer prices in previous auctions varied, but there are examples of hammer prices reaching up to 1250 euros (in 2015). However, there are also lower hammer prices, such as 110 euros and 150 euros in previous auctions.

Since there is no information about the condition of the current coin, it is difficult to make an accurate estimate. However, considering that the starting price is significantly higher than previous hammer prices, and that the average hammer price is 595.69 euros, a reasonable maximum purchase price could be in the range of 800 to 1000 euros, depending on the buyer's perception of the quality and demand for the coin.

Therefore, an estimated maximum purchase price could be 1000 euros. This allows the buyer to take into account the possibility that the coin may not reach the starting price and that the price history suggests a lower range.