Booting from one computer into another?

[ShadowTech01]

Title sounds a little weird so I'll explain. I just bought a Lenovo Legion Y540 RTX 2060. It's going to be my main computer whenever I'm on the road(which is a lot!), but I also have a more powerful self built pc at home. I took my SSD from my big rig and installed it in my new laptop. Boots and runs perfectly. It's great to use whatever I'm away from home or lounging in a different room. However, there are times when I need the extra power for my projects, but I want to keep them in one OS at all times. My Legion has a USB-C port(not Thunderbolt sadly) as does my big rig. Is it possible to connect the two via cable and boot my big rig from my laptop's SSD like a portable hard drive, or should I just swap the drive between the two? Having the drive outside the laptop like a passport is a no go.