Excess use of drugs will cause an overdose, which will result progressive damage until the status effect expires. Taking more drugs while overdosed will renew the overdosed effect.
The actual amount of doses that one can safely take depends entirely on Endurance. The following table reflects the dosage for those with 7 or less Endurance. Those with 8 Endurance can safely take one more dose before becoming overdosed (this is why trauma packs and Buffout can rise the potential maximum drug intake).