Is it okay to pray at a second Jumu'ah shift?

Yes, for most Muslims in the West it's fine. Many mosques run two or three Jumu'ah prayers because there isn't room for everyone at once. Most contemporary scholars and fiqh councils accept this as a need, and your Friday prayer at a later shift counts as long as it's within Dhuhr time.

Why mosques hold multiple shifts

In cities like London, New York or Paris, mosques are often small, rented or overcrowded, and many people only get a short lunch break. Offering a 12:30 and a 1:30 Jumu'ah, each with its own khutbah and imam, lets everyone attend. Allah made the religion free of unnecessary hardship:

وَمَا جَعَلَ عَلَيْكُمْ فِى ٱلدِّينِ مِنْ حَرَجٍ "...and has not placed upon you in the religion any difficulty." Quran 22:78

What scholars say

Classically, scholars discussed holding more than one Jumu'ah in a single town. The Shafi'i and Maliki schools originally preferred one main Jumu'ah per town and allowed more only when needed. The Hanafi school allows several Jumu'ahs in one city, and the Hanbalis allow it when there's a need such as lack of space. Holding repeated shifts in the same building is a newer question. Many Western scholars and bodies, including fiqh councils in North America and Europe, allow it because of real need, while some scholars prefer people to find a mosque with a single prayer if one is easily available. Both views are held in good faith.

Conditions for a valid shift

It's prayed in Dhuhr time, after the sun passes its highest point and before Asr.
Each shift has its own khutbah followed by the two-rak'ah prayer. See How many rakat is Jumu'ah prayer?
There's a proper congregation, not just one or two people.
Once you've prayed Jumu'ah, don't also pray Dhuhr; it replaces it.

Better than missing it

If the second shift fits your work or class schedule, it's far better to attend it than to skip Jumu'ah. The Prophet ﷺ warned that whoever misses three Jumu'ahs out of carelessness, Allah seals his heart (Sunan Abi Dawud 1052). A later shift is a blessing that helps you avoid that. If neither shift works, see Can I miss Friday prayer because of a lecture?

Can I pray it at home instead?

Generally no; Jumu'ah needs a congregation and a khutbah. If you're excused, you pray Dhuhr. See Can I pray Jumu'ah at home?

Key points

Multiple Jumu'ah shifts are common in Western mosques.
Most contemporary scholars accept them due to need.
Each shift needs its own khutbah within Dhuhr time.
A later shift is much better than missing Jumu'ah.

Tip: Check your mosque's website for shift times and arrive ten minutes early. Later shifts are often less crowded, and parking is easier too.