Max number of Series strings?

The 3 parallel string "limit" is my suggestion... 1x is ideal. 2x has been used to have "backup" (if one string fails, you can limp along on the 2nd string). 3x is my personal recommendation (maximum parallel string limit) that the various issues start to add up and make massively parallel strings something to really avoid if at all possible. (lots of batteries to fill, issues of current sharing between strings, each string should be fused/breakered, secondary effects from temperature, problems monitoring/debugging issues, etc.). People have put more 3x strings in parallel and have been happy with their banks--But I would suggest avoiding if you can.

Batteries in series... In reality, a "battery" is already a series of cells (3 in series for 6 volt, 6 in series for 12 volt, etc.). There is no basic reason you cannot put XX cells in series. There are some secondary issues that make this an issue:

1. You need to check / monitor cell/battery voltage. A shorted cell in a 6 volt battery means 4 volt operation--Easy to see. A 48 cell battery bank (96 volts nominal) with a shorted cell means 94 volts--Not obvious in a "working range" of 84 volts to 120 volts (near dead to equalization voltage).
2. High voltages--The battery case may not be rated for a >> high voltage bus voltage (12 volt battery in a 96 volt string would need to be tested to ~360 VDC to ground (~3x max operational voltage "highpot" test).
3. A lot of cells to check water levels...
4. More "devices", is more chances for failure.
5. Higher voltages, more chances that a ARC can form and cause a fire.
6. Higher voltages need higher voltage rated fuses/breakers--High voltage/high current fuses/breakers are not cheap and sometimes not easy to find
7. Higher voltages are more dangerous (electrocution hazard)--And any voltage over ~60 VDC is considered hazardous and needs to be in a locked cabinet or room (for commercial equipment).

So--To your question... 48 VDC nominal lead acid battery bank is about the highest working voltage a day to day type residential off grid power system is going to be designed for/installed. There are higher voltage AC inverters available (typically used in computer room installations and such)--But, not going to be "standard issue" for our use.

I also like to keep cell count down... I would not go with a 24 cell (48 volt) battery bank to power a smaller system. For example, a 1,200 Watt or less system can work very nicely on a 12 volt battery bank (with relatively large AH batteries--nominally a ~480 AH @ 12 volt battery bank minimum).

I would not usually suggest, for example, a 1,200 Watt inverter on a 48 volt battery bank. That is ~120 AH batteries (cell) minimum. It can  work--But you now have 24 cells to "water" and inspect vs 6 cells (and interconnects) on a 12 volt bank. But if all you can get are 12 volt @ 100 AH deep cycle batteries in your area--perhaps that is a "good enough" reason to go 48 volts (and if you can find a 1,200 Watt @ 48 volt input AC inverter, etc.).

Remember, Power=Voltage*Current. So, it is a balancing act... Perhaps for some reasons higher voltage is "useful" (i.e., long wire runs), or perhaps higher current with low voltage batteries is more cost effective (i.e., using 6 volt @ 200 AH golf cart batteries). Many of the rules of thumbs we use around here are "biases" towards certain choices/suggestions that usually work out for the best. They are starting points and can be "adjusted" for specific reasons/applications and when the advantages outweigh the drawbacks in your installation.

So, back to the basics... What are your load requirements? Watts, Watt*Hours per day, Amps at what voltage, Amp*Hours per day, etc.... What equipment do you already have (suggest paper design before buying anything).

-Bill