Double pumping stimulates milk production more than single.  It
can increase the supply, especially if there is more breast stimulation
overall. Double pumping also cuts pumping time in half.
How old is this baby?  Is the mom working or is she pumping for another
reason?
The pump matters, too--depending on age of baby and reason for pumping.
The pump you mention *may* not be appropriate for a baby younger than
six weeks with a mom who works full-time or nearly.
Is the mom pumping six times while she is separated from her baby? If
she's at work, I can imagine the double pumping would come in handy.
When she's home, the mom can increase the frequency of nursings.  She
can also try pumping while nursing the baby and switching.
Another thought--you say the mom is not keeping up with the baby's
needs.  How much is the baby taking when away from mom?  Could the
caregiver be feeding an unhappy baby more than the baby would be nursing
if he or she were with mom?

Diane, LLLL in VT