Ethically speaking, I would hesitate to make any recommendations without physically seeing this baby nurse.  If I read the weight gain description correctly, the baby gained only 6 oz between the first and second month.  6 ounces in an entire month is terrible--that's the minimum expected gain in one week.   Even if the baby breastfeeds "all the time,"  chances are the mom isn't reporting accurately, or doesn't understand milk transfer (baby mouthing the breast and never swallowing, or one swallow per 12 sucks etc.).
And weight gain shifted to a more normal level with supplementing.  So, until someone can observe the baby feeding, maybe explore the supplement.  Is she supplementing with her own milk?  Is this baby a candidate for an SNS?  How's the milk supply?  Safeguard milk supply and weight gain until she has time for an appointment.  "String bean" baby would have maintained his string-bean-i-ness if it had nothing to do with calories.
My $0.02.  :)
Amy Peterson, IBCLC

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