Can a woman with a hormone production anomaly drop a second egg after conception and get pregnant again? Suppose a woman , who is normally expected to have a sudden increase in progesterone levels that prevent conception is afflicted by a medical anomoly or illness that temporarily causes a misfire of the hormone production normally accompanying conception, due to some medical reason, could she thus have the abnormal effect of concieving twice in the same ten month period? 
This question assumes the answerer knows that women have all their eggs in supply alat birth and do not actually produce just one a month.  One is supposed to drop but sometimes two or three do and you get fraternal twins or trips. identical twins come fom same egg that splits for some reason. all women are not equal and all hormonal and biological processes are perfect or complete everytime. things go wrong. I do not ask if this is a normal thing, only if it is medically and biologically possible for it to occur under certain circumstances. Not  asking does it USUALLY occur or is it normal. This would be ABNORMAL

Summarized question: Is it possible for a woman to become pregnant a second time while already pregnant?