Your title... should it be "Layer 3 design?" Or are you referring to a 3 tier architecture?
In reference to your question... Yes, you can have vlan 20 as two entirely separate subnets (Im assuming closet=subnet in your explanation?) But they must be in very separate layer 2 domains. Also, even though this is very possible, its not a good idea at all!
Each person has their own concepts to build the best ip/vlan structure but to have one vlan in different layer2/3 domains... its not a good one. If it is working with something you inherited then attempt to migrate to a new vlan. If it is something you cannot change then there is very little you can do about that.
For example... our architecture is 10-999 prod, 1010-1999 is ilo, 2010-2999 is backup, and 3010-3999 is qad. This allows you to keep the vlan number the same but yet give you the flexibility of having all four tiers for one server. (I dont use the first 10 because you are not able to use 1000-1010 due to Cisco hard settings.)
