I routinely do. Originally, I was just keeping my "Old Faithful" Mach 3 in service, and using up a can of Barbasol. But I like Barbasol, so I bought more, and I bought more cart razors to try them out, so I added them to the rotation. Now I have certain days set aside for cart use.
I once retried the cart, maybe 3 month after jumping in the DE tsunami, it didn't impressed me. I also tried Barbasol with DE, it didn't impressed me I didn't touched a cart or a can of goo for about 18 months and I don't plan on ever switching back to carts.
The only reason why I'd use a cart/Goo again would be If I'm travelling in a place where I don't trust the water in the sink....or the sink itself !
I occasionally use both together, or a DE with Barbasol yellow, or a cartridge razor with brush/soap. It all worked good for gents in the Sixties and Seventies, and it works good for me.
I went back to the Gillette Fusion and goop once but just for body hair maintenance. I wanted to see how I felt about it after learning about wet shaving. It was ok for body hair removal but not as good as my Futur and TOBS. It tugged enough that I never felt inclined to try shaving my face with it again.
I still think Barbasol is about the best canned goo that America produces. It's not as good as a brush and a good soap, but it's pretty good considering it costs less than $2.00. The gels never worked well for me. I have a can of Proraso foam on the way to try out for kicks. I'd use Barbasol over some soaps I've tried. I throw the Sensor into rotation every so often so you never know; I could wind up using some Barbasol and the Sensor on the same shave someday.
I've never used a system razor nor any aerosol shaving anything.
started with a DE, brush, mug, and soap.
Got a couple of electric razors from well meaning relatives for xmas and bday presents but most got a quick buzz then put away and brought out to sit on the counter when the giver came visiting.
the closest I come to this is using a Schick I1 and a soap stick - I will never again use a cartridge or canned goo unless I have absolutely no wetshaving options available