Mothers who have been in the position of making this decision themselves say that the effects of injectable fertility medications on breast milk are negligible. From that point of view, it would technically be possible to undergo another cycle of IVF, either an egg retrieval cycle, or a frozen embryo transfer. But the problem with having invitro fertilization while you are breastfeeding is that the chance of a positive beta is much lower due to the hormonal impact of breastfeeding. For the same reason, many women find it difficult to conceive naturally while still breastfeeding an older child. No reliable studies have been conducted into the impact of nursing on IVF success rates, so any evidence that is presented is mostly anecdotal.
It would be very hard to find a reproductive endocrinologist who would be supportive of undergoing IVF while breastfeeding. And because fertility treatments are so expensive, and the success rates are likely to be much lower, this is not at all a popular decision. Women who were faced with the difficult decision of either having IVF again and weaning, or continuing breastfeeding but waiting with IVF, have to make a personal decision. Many do wean to be able to have IVF (again), especially of they are older women who want to have the best chance of getting pregnant again. Some do wait, and end up with a larger age gap between their children.