Can I power ESP8266 with more than 3.5 V?
The datasheet usually is definitive on the allowable range of voltages.

Look in Section 5.1: Electrical Characteristics.

Working Voltage Value:


Min: 2.5 V
Typical: 3.3 V
Max: 3.6 V


If you have to feed in signals that could go higher than 3.3 V in normal operation, you need to either clamp it with Zener diodes, or use a voltage divider. 

If you are asking about powering the chip with more than 3.3 V, don't. You can get away with a 3.3 V linear regulator and 2 capacitors so that you are powering it with no more than designed supply voltage.