I used to have a (very) few customers who needed special arrangements. I was happy to accommodate them.
The terms were: "Phone me when you want them doing, I will come straight away subject to finishing the job I'm working on at the time"
The price was: £X (my usual price for that particular spec of house) plus my 'Premium Service' surcharge of £50 per visit.
Most would reject the offer out of hand, a few accepted that special treatment meant a special price and accepted.