When you want redundancy for the network.

example:

L3 has three alternate way for the destination ,that scenario on the SVI interface

can configure three Ip ,if the link fails which has 1st ip traffic will automatically fallback to 2nd link which has secondary ip

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interface Vlan1

ip address 192.168.1.254 255.255.255.0 secondary

ip address 192.168.2.254 255.255.255.0

Usually the reason I've seen multiple IPs on a VLAN is IP migration or address exhaustion- if you're moving from one scheme to another, and can't touch every device at once. Let's say you're migrating from 1.1.1.0 / 27 to 2.2.2.0/24.

The old config was:

int vl 1

ip address 1.1.1.1 255.255.255.224

You would drop on this config:

int vlan 1

ip address 2.2.2.1 255.255.255.0

ip address 1.1.1.1 255.255.255.224

And now users on the old address scheme can still get to the rest of the network, until you have time to go touch their PCs and reconfigure.

You might do this when you need more IP address range within a physical cable plant, and can't accomplish this easily with downstream switches that don't support multiple VLANs or trunks, etc.

Yes you can, using secondary addresses, as shown in mtechnology's post.  NB: there are some issues in doing this, such, as by default, DHCP will only provide addresses to the primary address network.