A total of 67 families will be represented by the same legal team as they seek compensation over the scandal at Aberdeen's Hazlehead Crematorium.
Baby and adult ashes were mixed together at the crematorium and given back to relatives of the adult.
The parents of infants were told there were no ashes.
Aberdeen City Council announced in December last year that it had approved a new financial compensation scheme for those affected.
The deadline for claims has been set for 1 February.
BBC Scotland revealed in 2013 that no ashes had been offered to the families of infants cremated in Aberdeen over a five-year period.
It followed similar revelations about Mortonhall crematorium in Edinburgh, which had been secretly burying baby ashes for decades.
A report into the scandal by Dame Elish Angiolini described the practices as "abhorrent".
Thompsons Solicitors said they originally represented 21 families but that had risen to 67 as the compensation deadline looms.
Company partner Patrick McGuire said the compensation announcement was justification for the families "who had fought for years to get the council to acknowledge the wrongs done to them".
He added: "I have rarely seen such a large amount of people contacting us in such a short space of time.
"I think what this actually shows is the number of families in the Aberdeen area that have been touched by this scandal and have suffered in silence. They no longer need to do so."
Lawyers for parents affected by the Aberdeen baby ashes scandal said they have been "astonished" by the number of people contacting them for help.