I've just confirmed that this is doable now, as long as the two VPCs you're trying to multi-home with are from the same account and availability zone.
You can launch an EC2 instance in one VPC and attach a secondary ENI from another VPC (but in the same Availability Zone) to the instance. This enables you to create multi-homed instances across VPCs with different networking and security configurations. You cannot create multi-homed instances across VPCs across different AWS accounts. (https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/scenarios-enis.html#creating-dual-homed-instances-with-workloads-roles-on-distinct-vpcs)
UI Quirk (Nov 2023): I tried to use the "Attach ENI" feature of the Web Console UI to add a nic from a different VPC to an existing instance, and it wouldn't let me pick the ENI I wanted (despite the ENI being available, in the same account, and same AZ) -- it only let me choose ENIs from the same primary VPC as the first nic on the instance. I think that's just a Web UI limitation.
You can work around it in the web UI by creating a launch template, in which you add two network interfaces, and those interfaces CAN be from different VPC, no problem. If you launch an instance from that template, it will get (depending on your config) an address from both vpcs respective subnets.
I suspect that if you go about it from the terminal (using aws-cli), you can bypass this quirk and modify your existing instances too (in addition to launching new ones). But I've not confirmed.