Yes you can.
First take Token and go to counter. You will be rejected from counter..they will tell you to meet captain...
Dont worry

The captain is a Good man...He will ask you, is it 4th Month...he will approve...
I went yesterday to Onaiza Governement Service Centre...it was the 4th month extension...and the whole process just took 7 minutes when I enterered there at 2:45pm.

Go in the noon, you will find it almost empty.

For now get that 1 month extension...After your wife get admitted ...take the medical report from hospital and show to captain.. he will extend for 3 months more...but not now...dont discuss all this...simply say..it is 4th month extension...

May Allah bless you and your family and give u sweet children that benifit the ummah and everyone.