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1) You can buy water heaters with 5500 watt elements via the manufacturer. This will give you 4-7 gallons more hot water per tank vs 4500 watt heater, and might cost premium, but will be made with correct wiring and have full warranty support. Resource: Example spec sheet   Reliance spec sheet

2) You can convert ordinary residential water heater from 4500 watt elements to 5500 watt by replacing elements and get '4-7 more gallons hot water' per tank.

Math: Volts x amps = watts, so watts divided by volts = amp draw.  
3800 watt water heater ... 3800 watt divided by 240 volt = 15.83 amps ../. can use 20 amp breaker and 12 gauge wire
4500 watt water heater .. 4500 watt divided by 240 volt = 18.75 amp ../. by code ... use 30 amp breaker and 10 gauge wire
5500 watt water heater ... 5000 watts divided by 240 volt = 20.8 amp ../. must use 30 amp breaker and 10 gauge wire

Breaker rating is 80% rated value of breaker, called the safe maximum.
20 amp breaker x .80 (80%) = 16 amps .... note that 4500 watt 18.75 amp water heater is within 20 amps, but not within the safe maximum 16 amps.
30 amp breaker x .80 (80%) = 24 amps ... note that 5500 watt 20.8 amp heater must have 30 amp breaker.

BUT REMEMBER ... the internal wiring inside many 4500 watt heaters is the smaller 12 gauge wire, that will be inefficient and have higher incidence of burned, melted connections at thermostats and elements.

When thermostat is higher, then the tank holds more heat energy and lasts longer because you mix the hot with more cold at the tap to keep water at the 104-110°F temperature that is typical for shower, bath, hand washing. Resource: How to install under counter water heater
Less hot is consumed from tank with each bath-shower, and so less cold water enters tank per shower, water inside tank cools more slowly ...,. and overall amount of hot water produced by a fully heated tank is higher.
You can further increase tank capacity by using a tempering valve: Buy: Mixing valve Resource: Advantages-disadvantages mixing valve

If faster recovery is needed, or you need tank to reheat more quickly so more showers can be taken sooner, then higher thermostat might not solve problem because recovery has dropped below 31 gallons, and is now 27 gallons for 4500 watt element. Why? Because water heater must heat water longer to achieve higher 130°F temperature. All numbers are approximate and vary by condition of heater, incoming water temperature, thermostat calibration etc.
Thermostat calibration is +-5-8%.
Combining higher temperature setting plus 5500 watt element will give 33 gallon recovery. Resource: Recovery chart As a result, the first hour delivery (amount of hot from tank) is more than 7 gallons since the element is faster heating and the thermostat setting is higher.

1) There is a known and documented risk of scalding if water heater temperature is set over 120°F, especially with disabled people, older people and children who might NOT feel or respond to sensation, or have delayed response.
Resource Scald chart
2) Higher temperatures cause water to expand, putting steel tank under more pressure.
Resource: TP valve code and hazards
3) Closed system and high pressure: As long as tank is not rusted and ready to burst. there is no outright risk to the tank itself if temperature is raised, but if pipes are subjected to higher pressure because of specific plumbing problems, then the plumbing could be issue. Resource: Closed system
A bursted water heater or broken pipe can spew hot water all over a person, and flood home for hours when folks are at work.
Resource:  Prevent rusting and replace anode

(1) 5500 elements heat faster and put more strain on tank, causing warranty to cover issues that were not intended.
There is probably no measurable effect on longevity of tank itself by turning up thermostat or adding 5500 watt elements if tank is not old, rusted and ready to burst, since the TP valve and thermostat ECO (reset button or energy cut off) will protect tank from overheating and high pressure.
Resources: TP valve code  Prevent rusting and replace anode

BUT the electrical wiring could be issue, even with well-maintained tank, and would definitely affect warranty.

So 30 amp breaker and 10 gauge wire will safely support the 5500 elements.
But 12 ga wire and 20 amp breaker (sometimes found with older homes that are still within code that applied when home was built) will not work for 5500 watt. Do not upsize the breaker to 30 amp, unless wire is also changed to larger 10 gauge to match safe wiring codes.
Resource: Color code for wire and breaker

This is the point where the electrical problem arrives:
Water heater manufacturers often install smaller 12 gauge wires inside water heater that connect to thermostats and elements. To check your tank, buy short piece of 10 gauge solid copper wire from local hardware and compare size of copper with wire inside tank.

Calculation: 12 gauge wire has safe max 20 amp x 80% or 16 amps ... 16 amps x 240 volts = maximum 3840 watts ... so 12 gauge internal wiring is barely enough to support 4500 watt element. Meaning the 12 gauge wires inside tank are already running hot and inefficient. The problem is mitigated by the short length of the wires.
Since the load (water heater) is not 'continuously operating' then electric code allows manufacturers to do this since 12 gauge wire can carry the full 20 amps or 4800 watts before overheating. It's not best because heat means energy loss, and more potential for burned wire, or damaged element and thermostat ... but 12 gauge wire works safely for the 4500 watt heater, but is highly questionable for 5500 watt.

If your heater has 4500 watt elements then that's running the breaker and wire at cooler temperature than 5500 watt.
Heat is the enemy of all things electrical ... inching up wear and tear on breakers, busbar, power company transformer etc .,.. heat costs money, and all costs are energy
....Therefore, from conservation perspective the 4500 watt is better than 5500 watt.

Local codes vary widely and are usually more strict for commercial applications.
Typically, a residential water heater comes wired for non-simultaneous operation. This means either the top element is ON, or bottom element is ON, or both elements are OFF ... but at no time are both elements ON at same time. Resource: How electric water heaters work
The product label located on side of tank will show non-simultaneous.
Water heaters can be special ordered to meet other wiring objectives, such as simultaneous or off peak etc. The label and warranty would match the water heater.
If a heater is rewired for off-peak or simultaneous etc, then technically the owner of heater should apply to manufacturer for a new label. This is rarely done, and we know the manufacturer would never send a label. You might as well photoshop your own label and paste it on if desired.
The best route is to say nothing, since notifying the manufacturer would immediately void product warranty .. assuming someone at company was paying attention, which is also unlikely.
Resources: How to wire water heater thermostats    3-phase water heaters     9000 watt water heater
The same applies if you change element wattage. The label shows 4500 watt or 3500 watt etc, but if you change to 5500 watt, then the label should be changed to reflect the alteration. Of course contacting manufacturer or getting a new label would be sketchy unless manufacturer agreed ahead of time and work is performed by licensed technician ... but for commercial application, if a heater is altered, and doesn't have matching label, then some inspector might get overly enthusiastic and create a problem ... explaining why the issue needs to be mentioned.