The mistake I see most often
Organisations that already have ISO 27001 in place frequently treat ISO 27701 as a separate project. That's expensive, and it's not what the standard is designed for.
ISO 27701 is an extension, not a parallel system
It's structured as additional guidance and controls layered directly onto ISO 27001's management system clauses, plus PIMS-specific controls for PII controllers and processors.
Where the real work is
The genuine lift is in mapping data flows precisely enough to know exactly where you're a controller versus a processor, for which categories of personal data, and under which legal basis.
A practical sequencing note
I generally recommend organisations complete at least one full ISO 27001 internal audit cycle before layering on ISO 27701.
“If a control cannot be evidenced, it does not exist.”