"The basic entitlement available to each eligible Veteran is $36,000. Lenders will generally loan up to 4 times a Veteran's available entitlement without a down payment, provided the Veteran is income and credit qualified and the property appraises for the asking price."
The 4 is in reference to a calculation of the VA guarantee, not the number of homes a lender will lend on.
There isn't a maximum number of homes you can purchase using your VA loan, it will all depend on a multitude of factors including, but not limited to:
- your remaining entitlement (1st and 2nd tier) Here's a good post explaining the calculations in detail: https://www.veteransunited.com/valoans/second-tier...
- where the homes are located
- your intent to occupy the new home as your primary residence
- other circumstances like a PCS, upgrade in the same area, etc
Veterans United Home Loans specializes in VA loans is an amazing company (of which I work for, educating real estate agents about VA loans).