I haven't worn the newborn and the toddler together yet as DH is still off work and wears the toddler for me.

But I have worn two similar size kids before, twice. They were both about 20 pounds.
So once, I had mine on the back in the mei tai and put the other on the front in an Ergo. The other time I had one on the back in a mei tai and the other on the front (tummy to tummy hold) in a ring sling.
With a newborn you need to be careful that you aren't tying the toddler over top of the newborn, but you can tie the newborn over top of the toddler. But you can really use whatever carriers you want--mei tais, SSCs, ring slings, wraps, all seem to work, you just have to figure out the best order for putting them on.

I mean, you could put the toddler on the back in a ring sling (I've not tried that, but people do) and then put the newborn on the front in another ring sling on the other shoulder.
Or have them both in mei tais, with the toddler tied ruck style. Or have the newborn in a wrap and the toddler in an SSC or mei tai. Or...or...or...pick your favourite carriers, really.