Marcia Tuttle addressed this topic in an article that is in my department's
required reading manual.  It is "Magazine Fulfillment Centers: What They
Are, How They Operate, and What We Can Do About Them," LIBRARY ACQUISITIONS:
PRACTICE AND THEORY 9 (1985): 41-49.  Among the actions she suggests for
libraries are ordering directly from the FC rather than through a vendor.
For multiple subscriptions, create different addresses (i.e. Periodicals
Dept on one; Serials Dept on another) to avoid having the FC computer
combine them into a single subscription.  Claiming directly from the FC
even if the order is with a vendor is encouraged; EBSCO "blue card
claims" are very useful; this is a postcard-like claim with boxes to
check for desired action and a *place to attach the mailing label*.
The article explains how crucial the mailing label is; the FC can't
identify the subscription otherwise.
  Other tricks we've tried have been to renew for the longest period
your local system will allow-- like 3 years.  Since most of the problems
occur with renewals, this reduces the number of times that happens.  One
can do staggered multiple year renewals (like one third now for 3 years,
one third next year, etc.).  So far as direct renewals go, we find that
you can authorize the renewal notice for payment from an early notice and
then use the next notice to check the "please renew and bill me" or
whatever box.  We also prepare a list of FC titles and someone gets the
job of checking up on them regularly; prompt claiming is critical.  Hmmmm
anything else?  Oh, yes-- we try to check the expiration date on the
issues that *are* coming to note when the date changes without reason and
thereby avoid problems.  Also, if duplicates start, you can plan on the
subscription expiring early.  That's a case for the "blue card claim"
card box of "combine and extend".  We have also tried to poll staff to
find out who subscribes to FC titles and can be asked to donate copies
when claims are unsuccessful.
   Becky Lenzini, then at Faxon, was quoted in Marcia's article as
recommending concerted library action to demand better service.  On the
other hand, I've been told library subscriptions are less than 1 percent
of the volume of business but 30 or 50 percent of the problems-- so we're
no more popular with them than they with us.