This can encourage gazumping (where a higher offer is accepted over the original one).Some vendors would not have a problem with this. However, in practical terms it is often the case that once the original buyer falls away in favour of the new, higher, buyer, the new buyer feels the pressure is off, and they regret having offered more than the market price. Their offer is subsequently reduced (gazundering). This practice often serves to frustrate the vendor and even risk the sale. The first offer is usually the best offer.
However, there is no point in taking your property off the market if your buyer is not in a strong buying position or has a linked transaction. This latter situation reduces the saleability of your home to the saleability of any linked properties, over which you have no control. So our advice is generally only to remove your property from the market, perhaps for a fixed period of time (say two weeks to keep the pressure on the buyer to perform) when you have confirmation from the buyer’s solicitor that they have no linked sale, have their mortgage in principle and deposit available