You can book two separate tickets as long as you understand a few things.
1. It is two speparate ticktets so you are not protected should something go wrong. example. Ticket #1 your plane is 3 hours late or flight is canceled. Ticket #2 doesn't care and if you can't make the flight then too bad, you will have to see what the refund/exchange fees are (if any). Separate tickets will not protect you to get to your final destination should something happen.
2. You may be able to check your bags all the way through, or maybe not. It will depend on airlines, flight times, baggage allowances, ect. If you cannot interline baggage make sure you have enough time between flights to collect luggage and then check-in for the next flight.
I am sure there are more but these are two very important considerations.