Yes, the SKB Cases MIL-STD Injection-Molded Parallel Limb Geometry Bow Case will fit parallel limb bows up to 41" in length.
This would fit but would likely be too large. The SKB case for the V3 27 can be found here: https://www.skbcases.com/sports/sku.php?cat=12&pid=245&sku=3i-3614-MPL-M
The proper SKB case for the V3 31 can be found here: https://www.opticsplanet.com/skb-cases-mathews-iseries-bow-case.html
According to SKB, that case will not fit your bow and they suggest a lager case with part number 2SKB-4119 and in the following link - https://www.opticsplanet.com/skb-cases-ata-parallel-limb-geometry-bow-case.html
Here are the dimensions provided by SKB. It seems as though the case will be small enough:
Specifications
Interior Length: 40"
Interior Width: 14.5"
Interior Depth: 5"
Carton Length: 45"
Carton Width: 17.50"
Carton Depth: 6"
Shipping Weight: 23 lbs.
Specifications
Interior Length: 40"
Interior Width: 14.5"
Interior Depth: 5"
Carton Length: 45"
Carton Width: 17.50"
Carton Depth: 6"
Shipping Weight: 23 lbs.