STD from one or many?

Patient: I have been trying to find concrete information to provide my partner. The question of faithfulness has been brought up due to our recent contraction of an STD. At this point believed to be gonorrhea or chlamydia. Can you contract an STD if you do not currently have multiple partners? I understand with unprotected sex, coupled with anal sex the risk factor is higher. But with monogamy can you still get an STD?