Q: Can I use my VA eligibility to buy investment properties?
A: The answer is "probably not," or at least "not directly or immediately."
The VA will not back loans specifically made to acquire investment properties. The intention is that the benefit of the VA home loans program will be used for your primary residence. That said, there is a provision where you can rent out your primary residence and purchase another residence using any unused portion of your original entitlement, if you should have any.
This would generally be done if you moved or were moved due to a change in your “permanent change of station” (PCS). You would use this unused portion to help fund the purchase of a new primary residence, while your "old" residence could be rented out rather than sold.
If the property of your primary residence is a multi-family building and you intend to remain living in the unit and purchasing the others from existing owners, the answer is much closer to “yes.” You would purchase the home and occupy one of the units. You could move on from there, rent out the unit you occupied and possibly purchase another home using any remaining eligibility. More likely, you would have little eligibility left and would need to refinance to a traditional investment property mortgage, which would pay off the VA and restore your eligibility... and you would have an investment property that was (at least initially) funded by the VA program.
To learn more about buying apartment buildings, read "How to buy and finance apartment buildings."