Guests asking for significant discount off rate - new host advice required

Received a request from a booker for almost 50% off my regular rate - said we're only willing to pay X per day all in for a group of 8 adults for 5 nights during the late August timeframe.

I offered them 35% off plus taxes (was running a new host 20% discount anyway) with an ask a positive review and to treat the house with courtesy. This is also our own vacation home that has been significantly remodeled.

His response was "we are not willing to commit at this time and will come back later".

I have 5 rentals already locked in for July and August. As much as I'd like to rent more, I'm concerned about lowering the rate too much and attracting the wrong guest. So far have been seeing families with kids, which is the right demographic for the location.

First, have any of you seen requests like this? What would you have done?