Lightening already bleached hair.

Naturally I'm between a level 4 and 5, I let my hair grow out until I had no box dye left on and then had a very full head of highlights put in (about 90% of my hair bleached out). I then had a toner put on it and, whilst I did love it, I did ultimately want to go lighter and eventually tone it to a smokey grey colour. I went back several weeks later and we decided that the best way of doing it was to bleach out all of my ends, we left out about an inch or less of my root. I then had a toner put on with 20 vol, it was the most dark grey shade from the Dialights collection. It wasn't grey enough for me and unfortunately it washed out after just one wash with just purple conditioner. I then went back the next week and had it retoned for free using a different colour (I'm presuming from L'Oreal again, they only advertise their use of L'Oreal and GHD products) but 20 vol again. The colour stuck a lot better, at first it was a very very dark grey which almost had a brownish tint in some lights, that has slowly faded or over the weeks and now it's back to the beige/silvery/muddy blonde that it was after my first tone. My hair was only bleached out to a bright yellow, I'm dying for the same colour which is all over Instagram where it's very very obviously grey and unnatural.
What's the best way of going about it? Bearing in mind that it's been bleached twice and I don't want it completely frying, my hair is quite dry now and I do get a fair few split ends but I wouldn't say it's at risk of falling out. Do I bleach and tone it again? Do I use a colour remover and then bleach and tone? I'm not sure of the best way of doing it without causing any unnecessary stress on my hair (or bank balance)!