When KVM (on Intel) virtualizes another hypervisor as L1 VM it does not verify that VMX instructions from the L1 VM (which trigger a VM exit and are emulated by L0 KVM) are coming from ring 0.

For code running on bare metal or VMX root mode this is enforced by hardware. However, for code running in L1, the instruction always triggers a VM exit even when executed with cpl 3. This behavior is documented by Intel (example is for the VMPTRST instruction):

(Intel Manual 30-18 Vol. 3C)
IF (register operand) or (not in VMX operation) or (CR0.PE = 0) or (RFLAGS.VM = 1) or (IA32_EFER.LMA = 1 and CS.L = 0)
 THEN #UD;
ELSIF in VMX non-root operation
 THEN VMexit;
ELSIF CPL > 0
 THEN #GP(0);
ELSE
 64-bit in-memory destination operand ← current-VMCS pointer;

This means that a normal user space program running in the L1 VM can trigger KVMs VMX emulation which gives a large number of privilege escalation vectors (fake VMCS or vmptrld / vmptrst to a kernel address are the first that come to mind). As VMX emulation code checks for the guests CR4.VMXE value this only works if a L2 guest is running.

A somewhat realistic exploit scenario would involve someone breaking out of a L2 guest (for example by exploiting a bug in the L1 qemu process) and then using this bug for privilege escalation on the L1 system.

Simple POC (tested on L0 and L1 running Ubuntu 18.04 4.15.0-22-generic).
This requires that a L2 guest exists:

echo 'main(){asm volatile ("vmptrst 0xffffffffc0031337");}'| gcc -xc - ; ./a.out

[ 2537.280319] BUG: unable to handle kernel paging request at ffffffffc0031337