I use Barclays along with Monzo and manage both via Emma. I did go Full Monzo for about 4 months but found this Barclays+Monzo combination better suited for my needs.
I have 5 direct debits out of Monzo and I pay regular amounts into my Monzo account for everyday use so its like half-full-Monzo.
Barclays is good because I have to get some regular payments from Middle East and they pay me £11 just for being with them (£14 for blue rewards minus £3 fee) every month.
When I decided to go back to legacy bank back in January there were quite a few things missing at Monzo so now I am considering moving everything back to Monzo in next few months quite seriously.