I believe Frances means that 2♣ is still a puppet to 2♦, but then any subsequent bids show an invite with 5-cards in the major. This is certainly what most England Juniors would be playing if you said "Two-way". I don't think 2N as a puppet to ...
We play 1♣ - 1R - 1M as multi with 11-13 bal. or lots of mid-range support options or FG ♣:
1♣ - 1R - 1M
2♣: inv relay
2♦: FG relay
2N: 4M, inv. opp. 11-13 bal
3m: 4M6m inv. opp. 11-13 bal., but we can bid it on ...