Our basement slop sink needs replacement washers, but has no shutoff. So I went to shut off the house water supply, but the water does not stop even when I fully tightened the valve. Any suggestions from here?
Is your supply from a private well or some company or the city?
It is the inside shutoff of the municipal water supply. There is a water meter box on our front lawn that is between the main and the house.
There's probably a 1/4 turn valve in or near the water meter box. I'd turn off the water there and then replace the inside shut-off with a 1/4 turn fully ported ball valve.
A word of caution...
If there is a water shutoff in the meter box or on the meter assembly it may belong to the city. If you break it be ready to bend over for what they will charge to repair it.
Regardless, during the impending repair replace the failed valve with a 1/4 turn ball valve and add another valve inside the house where the water service enters.
The failed valve is the one inside the house where the water service enters. I am convinced that the best bet is to have a professional plumber replace it. They will have insurance if they screw up the valve at the water meter.
I know of one city where it is a misdemeanor for anyone except a city employee to open or close the valve at the water meter.
You also need to realize that even after closing the main valve there is a lot of water remaining in the lines, and it will drain out from the lowest valve.
Open the highest valve and lowest valve and wait for the line to empty.
Contact the municipal water supplier and they will dispatch someone to come turn the service off at the curb stop, then when you have completed the repair you contact them and they will turn it on again.