With modern medicine, terrific prenatal care, and a woman in good health, twins and triplets usually turn out well.
Quadruplets are rare but more common with modern fertility treatments. Survival is good.
No quintuplets survived until 1934. Modern care is essential.
It took until 1983 to get surviving sextuplets. Only 4 sets have ever existed in the world.
The record for surviving multiples is octuplets. Several sets were all born alive but only one set survived past infancy (and is still alive, at age 10).
For higher numbers:
There have been a few sets of nonuplets (9) in which a few babies were
born alive, though none lived longer than a few days. There have been
cases of human pregnancies that started out with ten, eleven, twelve
or fifteen fetuses, but no instances of live births. The pregnancies
of the 10, 11 and 15 fetuses have all resulted from fertility
medications and assisted reproductive technology (ART). However, there
has been one documented case when 12 fetuses were conceived naturally.
The most common complication for multiple births, including twins, is prematurity. But there are other health risks as well. And of course stillbirth is not uncommon:
Multiples are also known to have a higher mortality rate. It is more
common for multiple births to be stillborn, while for singletons the
risk is not as high. A literary review on multiple pregnancies shows a
study done on one set each of septuplets and octuplets, two sets of
sextuplets, 8 sets of quintuplets, 17 sets of quadruplets, and 228
sets of triplets. By doing this study, Hammond found that the mean
gestational age (how many weeks when birthed) at birth was 33.4 weeks
for triplets and 31 weeks for quadruplets. This shows that stillbirth
happens usually 3–5 weeks before the woman reaches full term and also
that for sextuplets or higher it almost always ends in death of the
fetuses. Though multiples are at a greater risk of being stillborn,
there is inconclusive evidence whether the actual mortality rate is
higher in multiples than in singletons.
The risks to the pregnant women go up too. High blood pressure, placental abruption, gestational diabetes, and anemia are all elevated with pregnancies of multiples. Placental abruption can be fatal to the woman, even in a hospital setting and high blood pressure increases the risk of eclampsia, which can lead to seizure or stroke and be fatal. Another risk is postpartum hemorrhage, which is treatable but potentially fatal (quite fatal outside of modern medical care if the mother is not transferred to a hospital promptly).
Also, these days, most twins are delivered by cesarean section. Essentially all triplets and higher are. While surgical delivery is becoming all too commonplace, it's not benign. The maternal death rate for c-section is 0.1 per 1000 operations in the UK and a whopping 5.43 per 1000 operations in a study of 22 countries in Africa. The in-hospital mortality of babies after Caesarean delivery [in Africa] was double that of high-income countries.
In the United States, surgical birth increases the risks of mortality (which are still fairly low) and complications, including long-term ones like hysterectomy and more (way too common) as compared to vaginal birth, even after accounting for serious risks factors requiring c-sections (a small percentage of the total for surgical birth).
If your setting is a time and place without modern medical care, as well as prenatal care to determine things like number of fetuses, position, placental status, etc, then survival rates are going to go way down.
Twins are usually not a problem and, until very recently, delivering twins was part of every OB's training (now they don't even get that training! at least not in the US).
You'd have a fair shot at triplets.
Quadruplets are really pushing it but it's possible. I wouldn't assume things would be okay but, if you want to create a story with quads, you could be on solid ground for that exception.
Quints and higher without modern medical care? Forget it.