I'm so sorry to hear that. MC, no matter how early is devastating. You ask if anyone else has had 3+ mcs - I have had 6 early MCs & 1 healthy baby & another on the way, due in a couple of months.
I had 4 early MCs, all between 4 & 6 weeks, before DD1. It was the most difficult period of my life without a doubt. An awful lot of people haven't the faintest idea why early mc would be so hard to deal with. Unfortunately it's rather taboo & the business of not anouncing pregnancies until 12 weeks contributes a little to that taboo so I think that a) when you miscarry you are unprepared having never heard about it and that b) people are often not very supportive.
Eventually I had investigations & as soon as the investigations were underway I conceived my daughter, who stuck, and thousands of knicker checks later arrived safely. They never found a cause. After her I had an accident (got pregnant when she was 5 months old accidentally) and no sooner had I discovered this & decided that, though it wasn't what I would have planned I did want the baby, than I miscarried that one. I had one further miscarriage as soon as we started ttc but then conceived my current bump straight after.
So yes I have had 6 mcs, no cause has been discovered & I have no real reason to believe I am anything other than unlucky (although lucky, now in that of course I have conceived 2 sticky ones for which I am eternally grateful). Part of me (the part no doubt, that just needs a reason) is convinced that I can't carry boys but I don't have anything very scientific to back that feeling up.
I know how hard it is to believe it, but the overwhelming chances are that you will keep trying, nothing will be found to be wrong with you (or if it is it will be easily fixable) and you will go on to give birth to a healthy baby. I swear I didn't believe that no matter how many times I read it - but my daughter is the proof of it.
I don't suppose anything can console you at the moment, but I hope that in attempting to answer your question I might be able to give you some hope.
Have you thought about doing something to honour the baby? I found marking each loss helped me to grieve and move on.