Joining the ''Eid Salah in the second rakat

What is the ruling in the Hanafi school of one joins the Eid salat in the second rakat? Should they still join? Do they have to do multiple takbirs in their make up rakat?

In the name of Allah Most Compassionate Merciful
I pray this finds you in ever increasing iman.

Yes one will still join the Eid Salat. So if he joins in the second rak'ah one will not say the takbir then, but when one stands up to perform the missed (first) rak'ah then one will say the missed three takbirs of the first rak'at after the recitation i.e. fatiha and surah with the other three second rakat takbirs.

If one joins in the second rak'at after the ruku then one will say the six additional takbirs in their respective place i.e. first (before recitation) and second rak'at (after recitation).

(Allamah Sayyid Zuwwar Husain Shah, Umdat al-fiqh, page 465 V.2)

And Allah alone knows best

Assalamu alikum