Nope! For various reasons, including that the IdenTrust cross-signature has a path length constraint that doesn't allow any longer chains for this path. Also, L

Nope! For various reasons, including that the IdenTrust cross-signature has a path length constraint that doesn't allow any longer chains for this path. Also, Let's Encrypt doesn't want to be responsible for supervising the correctness of your CA's operations. In theory this could be practical if you look at name-constrained delegations but it seems to me that there are a lot of practical problems with making this widespread. If you happen to be interested in discussing them in more detail, come over to https://community.letsencrypt.org/ https://community.letsencrypt.org/ and create a new "Issuance Policy" thread and we can get into it in more depth. But the short answer to your question is simply no—Let's Encrypt doesn't offer this service, isn't currently permitted to offer this service, and isn't interested in offering this service.