On a level 3 highlifts will usually be far too warm, unless you have a highlift brown designed for darker bases, but I haven't use one of them before. Or maybe something like Aveda Full Spectrum Deep where you can control the ammonia and the amount of tone.
When I have taken a level 3 to a 7, I prelift the hair first with a level 10 colour until it is a level 6 and then recolour with a level 7 colour and the appropriate ash tone and 20vol. This way you will get enough lift but also get the full colour deposit that you lose when trying to lift too much in one go.
On some hair types you would get it to a level 6 with 30vol but would just need to add in some extra mix tone to control the warmth.