The plunger only guts off the gas to the main jet, nothing more or less.
Crank it and let it die, then pull the plug and see if it is wet. If so, the float needle is not working to cut off the gas after the float has risen to max bowl level. You will have to CLEAN the cylinder that the float needle slides in, the sides of the needle, and make sure the tabs on the float that the needle fits into have zero build-up. I have had to pull a carb back off after I thought it was clean. So, I use some 400 grit emory cloth to polish the needle cylinder until its a shine.
If the plug is dry, you are not getting enough fuel, likely a jet is plugged. Use some carb cleaner, air pressure, and a tie wire to make sure all is open.
ps- Change the plug first before doing anything.:thumbsup: