Incandescent lightbulbs won't work very well when conected in series using normal mains voltages. At best they will illuminate dimly.
If your current single 75w lightbulb is on a dedicated 15A circuit, that would be surprising. Perhaps it shares a circuit with one or more wall sockets.
For safe/reliable operation you have to be sure that the total load on that circuit does not exceed 15A. So you need to sum the currents that are likely to be concurrently drawn by each of the parallel loads.
You must also connect your new light-fittings using wire of the construction and gauge specified by local codes (you didnt say if you live in Dhaka, Melbourne or Aberdeen). Connection methods and enclosures (junction boxes) also vary by region.
Using LED lightbulbs will enable you to provide your desired higher light output (lumens) without increasing the power used (watts) or, equivalently, current drawn (amps).
Unless you are happy to spend enough time to learn all this, you might be better off hiring an electrician, it might not be expensive if you do the decorative work, making holes for fittings and cable runs, making good and repainting.