Some good suggestions already, but I'll chime in since I've been chasing this sound for a while. What I think is really essential is parallel processing, so you can make the secondary signal sound unique from your primary bass tone. As someone mentioned, putting each signal through a dedicated bass and guitar amp would be ideal, but carrying that much gear may not be ideal. If your bass amp outputs a sound close to full range (a fair amount of high end) you should be good. I have a GK combo and it does very well at this. You just need a way to recombine the signals after splitting and processing. I've had success with Saturnworks mixer pedals (active with bass mod) for this.
For that secondary, "fake guitar" signal, you'll likely want a pitch shifter, distortion/fuzz/OD of some sort (smooths out the chirpiness of the pitch shifting), EQ of some sort (cab sim maybe), and maybe a touch of reverb. Others have mentioned using an 8 or 12 string bass. I've tried both and they mostly just sound like adding a chorus effect. Using distortion helps but that doesn't really separate the signals and trick the ear into hearing distinct instruments. However, using one in combination with a split, pitch shifted signal creates a huge sound but not completely necessary.
I have two pedalboards that I use for this. The first one I built is big, expensive, and daunting to take anywhere, even for jam sessions. The routing is a bit insane. It's full digital and midi controlled and also does a million other things. That one stays in my home studio now. I also built a smaller, hybrid analog/digital board for playing live and that has a parallel blender/mixer pedal, a pitch shifter/fuzz pedal, a digital multi-effects pedal, and a harmonic booster (EQ) pedal at the end. I can do more with the big board, but the smaller board gets me where I need to be. With either though, I have to be mindful of the phase relationship of the signals so I don't lose my tone.
Not gonna lie, it's a bit of sandbox (or quicksand) to play in, which can be very entertaining, but it can also be time and money consuming. I went through a variety of pedals and configurations before I settled on the boards I have now. I wanted to accomplish what Mike Kerr does but with a smaller footprint and not sounding exactly like Royal Blood.