Hi,
I read your posts and am so sorry to hear about your losses. I had 4 mc's!! And now am happily pregnant almost 25 weeks with twins

I went through the infertitliy work-up after 2 mc's and that is becoming the standard rather then waiting until 3. On average, work-up involves - blood clotting panel, anti-body panel, imaging - usually hsg, karyotyping (chromosomal analysis), luteal phase defect workup (biopsy), hormonse panel. Even after all that at mc #2, they missed a very simple problem with me. I had a septum that can increase mc rate up to 85%. I also had high fsh, and luteal phase defect. My current RE was suspicious of a uterine septum when he learned the shape of my uterus was arcuate (heart shaped) and a simple hysteroscopy found it and he removed it. My prior RE had attributed everything to high fsh (12), but in your early 30s studies haven't proven a correlation between that and poor egg quality Poor egg quality is a very common reason for mc when you are older or have had various treatments (chemo) etc.
Anyway, I am totally rambling and hope I haven't thoroughly confused you. I am glad I got tested. A simple start could be the blood work for the most common causes of recurrent mc (like blood clotting issues) and you could go from there. You may get pregnatn in the mean time

I got pregnant quick my first 2 pregnancies naturally. The rest were with meds.
Have hope!!!! If I'm sitting here with 2 very healthy twins after 4 mcs (plus one ruptured ectopic) it is very possible. I wish you tons of luck and loads of babydust.