A 4 engined aircraft with 3 inop engines will not be able to maintain altitude.
A one engine out scenario during the takeoff roll after V1 is the worst case engine out scenario, whether the plane has 2, 3 or 4 engines. If one more engine should shut down on a quad, IIRC the certification rules state that the (comercial) plane needs to maintain altitude, and this is a problem is you are on the runway on your way into the lights. So even if two engines out are worse than one, your options just went from some to "absolutely nothing I can do". If you are at altitude, your options are of course better.
1 engine is routinely practiced. If 2 engines out on a quad are I do not know.
"Loiter shut down". As you say, quads are built to cruise most economically with four engines turning. The exception is certain long range patrol aircraft like the Orion that gain more range at moderate speeds with two engines shut down.
"There are no stupid questions, but there are a lot of inquisitive idiots." - John Ringo