My main char (not this one) has all 4 major faction above 8. This is only possible by playing the epic arcs over and over every 3 months. In the Minmatar and Caldari arcs there are a few missions where you need to be careful to not lose standings with Ammatar or Gallente.
You can still play Level 4 missions but you need to deny all missions where you have to fight against one of the empires. Trouble is that you can only deny one mission for free every 4 hours. Otherwise you will lose standings with the agent, the corp and the faction (very tiny).
Most missions are against the pirate factions (Blood Raiders, Serpentis, Sanshas, Angels). If you don’t mind to lose standings with them, you can still play those missions. Some missions are against Drones or Mercenaries and you will not lose any standings.
Oh, and as Geo Eclipse Oksaras already said: Always deny storyline missions, because they have a huge impact on faction standings.
Other activies like Abyss, Exploration or wormhole ratting are free of standing losses. Mining also, except you kill belt rats which will affect standings with their pirate faction and corps.
My personal advice is to not care too much about standings. You just restrict yourself from playing a lot of very profitable missions. Or from denying missions you really don’t want to play. Or from participating in faction warfare. Try to see faction standings as some sort of resource/buffer to work with.
Ask yourself: Why you want these high faction standings? To be able to accept all Level 4 missions? Once you have the corp standings above 5, your faction standings only must remain above -2 before the agent stops talking to you. And keeping the faction standing above -2 is not that hard. Just switch to an agent from the other side from time to time and play their storylines to rebalance the standings. Or use the SoE arc to fix standings.
The only benefit of really high faction standings is the reduction of broker fees in NPC stations. You can reduce your broker fee to 1.5% with the broker skill alone. Another 0.2% by grinding the base corp standings to 10. And by another 0.3% for grinding the base faction standing to 10. Or you just use player built trading stations and your empire standings won’t matter at all.
It’s much easier to create dedicated market alts if you really want to optimize trading to that level. Grinding one faction to 10 is much easier if you don’t need to maintain standings with the others.