In the long run, the obvious step is to integrate local services on the Liverpool-Runcorn line (whether to Chester or Crewe) into Merseyrail, with Merseyrail-like frequencies (at least 4 TPH to Runcorn, and 2 stoppers each to Crewe and Chester from there), and similar steps taken with the other local services into Lime Street high level (which would then have more than enough room to accommodate long-distance trains).
That would require the Edge Hill Spur or something like it to be built at the Liverpool end. But that project is 50 years overdue as it is.
These local services should be in addition to hourly longer distance trains to North Wales, and via the Marches to South Wales. Hopefully the Crewe line, and the 2 track Weaver Junction-Winsford section in particular, will by then have been bypassed by a new high speed line.
No doubt in a moment someone will come along and question the demand. In response to which, I would point to the well-patronised 4 TPH services Merseyrail run on their existing lines.