Vlookup with Multiple criteria in different columns

[dgross]

Item #	Manu #	Vendor #	New #
46118 <tbody> </tbody>	1650 <tbody> </tbody>		3963-535 <tbody> </tbody>
46973 <tbody> </tbody>	0531005FG	07-397-6396 <tbody> </tbody>	2540-145 <tbody> </tbody>
	<tbody> </tbody>	07-090-0035 <tbody> </tbody>	4779-073 <tbody> </tbody>

<tbody>
</tbody>

I need to pull the "new #" based on either getting a match from columns A through C. I would like to use a vlookup that says if there is an item # give me the new # but if there is no item # in the column then find the Manu # and give me the new # and if there is no manu # then match the vendor # for the new #. I already created this formula:
=IF(IFERROR((VLOOKUP(A2,Sheet2!$A:$D,4,FALSE)),(VLOOKUP(B2,Sheet2!$A:$D,4,FALSE)))=0,"",IFERROR((VLOOKUP(A2,Sheet2!$A:$D,4,FALSE)),(VLOOKUP(B2,Sheet2!$A:$D,4,FALSE))))

How can I add in a vlookup for C2?
Sorry for the format but I didn't know how to copy and paste in my excel

 

[gaz_chops]

Try it with just iferrors
=IFERROR(VLOOKUP(A2,Sheet2!$A:$D,4,FALSE),IFERROR(VLOOKUP(B2,Sheet2!$A:$D,4,FALSE),VLOOKUP(C2,Sheet2!$A:$D,4,FALSE)))

 

[dgross]

Perfect, thats a much simpler way to do it!!!!

Where in the formula can I add that if it comes up to #N/A so leave it blank?

 

[dgross]

Never-mind i just added another IFERROR instead of just a regular Vlookup on the last part

 

[gaz_chops]

You're welcome and thats what i was about say

=iferror(IFERROR(VLOOKUP(A2,Sheet2!$A:$D,4,FALSE),IFERROR(VLOOKUP(B2,Sheet2!$A:$D,4,FALSE),VLOOKUP(C2,Sheet2!$A:$D,4,FALSE))),"")