Having written a TL on this subject I might be helpful... (note: the TL had a surviving Russian Alaska including Haida Gwaii, as well as Russian Alta California).
Well, you'd need to make the pre-existing Russian America, namely Alaska, more profitable in the long term than it was in OTL. Alaska was profitable in the beginning, being a new source of furs. However unregulated hunting made it unprofitable, so you'd need to bring a gold rush into the area while the Russians are still around.
Also an easier supply route would help. The Russians tried to establish control over the Hawaiian Islands in OTL (with Kaua'i being the center of Russian trade activity in OTL) and if they succeed the long transport route would be safer and an all-time Pacific warm water port would be available (to some extent, but it could provide a resting stop in the winter months during which Vladivostok was still frozen).
Also the southernmost part of Russian America was Port Ross near San Francisco. So... I'd say, "realisticly" speaking Russian America could cover portions parts of Western Canada (Manitoba and areas in the Hudson Bay drainage basin would still be British), focused on OTL's British Columbia, as well as the remainder of Oregon Country/Columbia District, as well as northern California up to San Francisco Bay, as well as northern Nevada and northern Utah. But that is the absolute maximum and it would require serious weakening of the US and the British.