Can a M$^blood even become a pureblood? (From Assumption)

[Susan]

No: HPFGUIDX 97810

Mandy Croyance:
Inbreeding would become even more integral to the functioning of such
a society and deformities aboud. As far as we know the wizarding
world is nowhere near the size of the muggle world and the number of
pure-blooded families is painfully small. It has already been said
that wizards would have died out had they not married muggles.

My question:
Is it possible for a m$&blood family eventually to become a pureblood 
family?  Ok, James is from a pureblooded family.  Lily comes from a 
muggle family, but she's obviously a wizard.  They have Harry.  Isn't 
he (Harry) technically more "pure" than Lily (bloodwise)?  So if he 
married a pureblood, their child would be even more "pure" wouldn't 
he/she? And if that child grows up and marries a pureblood...  See 
where I'm going?  Where does it end?

Susan