Newbie: current source; current sink for relays

I am trying to drive 28 relays with an Arduino through 4 74HC595s each driving a ULN2803 to control the relays. The relays will each draw about 150mA, and no more than 2 will be energised per ULN2803 at a time. I have read conflicting information about the ULN2803 from various sources, but it appears that it can handle 350mA per channel. I will be connecting an external power supply up to the arduino and to power the ICs. I have included a simplified circuit diagram.

Does this look like the ULNs will be able to handle the load?

Thanks for all comments/help.

Texas instr. can handle peak 500mA (one channel)
Be sure those 2 relays dont exceed 200mA each., U'll be safe.

Head problems occur if the IC id driven to hard. max op. temp 85 deg C

Your 'schematic' can work

Use a part that combines the HC595 and ULN2803 function: TPIC6B595
"Eight Power DMOS-Transistor Outputs of 150-mA Continuous Current"

Higher current versions are available also:
TPIC6595 Eight Power DMOS Transistor Outputs of 250-mA Continuous Current
TPIC6A595 Eight 350-mA DMOS Outputs
TPIC6D595 Eight 100 mA DMOS outputs (well, not this one)