You can have as many mortgages as your income and credit will allow you to be approved for. For the majority of individuals, one mortgage is all we can handle financially, but wealthy individuals often take out loans on several pieces of property at the same time. It is also possible to take out a second or a third mortgage on the same piece of property that you currently have mortgaged.
Assess your credit score and income. If you have sufficient income to make the payments on the additional mortgage, and funds for the down payment, then go ahead and apply for the additional mortgage.
Apply for any additional mortgages one at a time, preferably at least six months apart. Spreading new loans out over time minimizes the impact of the new loan(s) on your credit score.
Keep in mind that most banks will expect you to make a significantly larger down payment on a property that is not your primary residence (i.e. investment or vacation property), in some cases as much as 25 percent (even if you have good credit and fully qualify for the loan).
Veterans can get multiple VA loans. It is relatively rare, but possible for a veteran to have more than one mortgage through the VA loan program depending on local county regulations, the cost of the homes, and individual financial circumstances.