To estimate a maximum purchase price for the coin in question, we can analyze the provided data, including the starting and hammer prices from previous auctions, as well as the condition of the coins.

1. Current starting price: 150 euros.
2. Average hammer price in the past: 111.84 euros.
3. Previous hammer prices:
- They have sold for prices ranging from 20 euros to 550 euros, depending on the condition.
- Coins in high condition (95-100) have reached hammer prices of up to 550 euros.
- Coins in average condition (75-85) have had hammer prices ranging between 40 and 110 euros.

4. Condition of the coin: There is no information about the condition of this coin, which makes the estimation more uncertain.

5. Price trends:
- Coins that have had a starting price of 150 euros in the past have had hammer prices that vary, but some have reached up to 420 euros.
- The general trend shows that hammer prices can be significantly higher than the starting price, especially if the condition is good.

Given that there is no information about the condition of this coin, and considering that the starting price is 150 euros, an estimated maximum purchase price could be in the range of 200 to 300 euros, assuming the coin has an acceptable condition and that there is high interest in the auction.

Therefore, an estimated maximum purchase price could be 250 euros.