You can be a co-borrower on the property that your father owns. Some Banks require that you also be part owner of the property, some banks do not require this.
You can take a home loan for a new property, normally Banks will ask you of all your current loans [auto/other home/personal/ etc] to determine the amount they will be ready to lend.
Edit:
The first loan I believe your father already has a property in his name ... your father can apply for Loan against property ... if he does not have sufficient income, then you can guarantee the loan [ie co-sign on the loan, some banks allow this ... however there is no tax benefit on this loan] .
The second is the Home Loan for the balance amount that you would get it …
Both the loans can be taken from the same Bank, there would be a overall cap as to the amount of loan a Bank would give depending on your income, further the finance for this house will only be to the extent of 80% of the value.