So when we're discussing Oxygen Toxicity, it's important to note that we keep the terms correct and for that reason, we're going to talk about partial pressure. That is to say, the part of the pressure that relates to O2.
In other words; if at sea level the atmospheric pressure is 1 bar, and O2 comprises 21% of the atmosphere, then the partial pressure of O2 for our purposes is 0.21 bar.
This is an important consideration as when we get to the point of considering O2 as a problem, we're not considering it AND something else or O2 in combination; we're purely talking about O2 as a damaging agent and tests have proven that it's the partial pressure which is concerning, NOT the dilution rate of the O2 in atmosphere.
That said; the already provided link will show that the first thing you have to be concerned about is your lungs. High O2 partial pressures will also fry your retinas and cause neural damage, but it's your lungs which will suffer first. Anything above a PP of 0.5 bar is a problem.
When the Apollo astronauts flew to the moon and back, they did so in a pure O2 environment. That was very dangerous in terms of sparks igniting the atmosphere in the cabin, but for the pilots themselves they suffered no real issues with it. Why? Because they dialled down the atmospheric pressure. By dialing down the atmospheric density to (say) 0.4 atmospheres but making it pure O2, you put less pressure differential between the inside of your ship and the vacuum of space and you carry less weight into space for breathing gasses over the duration of the mission.
Getting rid of CO2 is actually the limiting factor for cramped conditions over time; anything more than about 1% CO2 causes more problems than does O2 toxicity in the short term. So; provided you can scrub the CO2 out of your O2 environment, your ship's walls can be thinner, the breathable air lighter; there's a lot of reasons to do that.
But in your case, you're talking about increasing density. So; provided the density of gas increases; the best solution is to decrease the proportion of O2 equivalently and you're good. At worst, don't let the differences get to more than double a conventional Earth-like atmospheric distribution.
Example; going to 1.15 ATMs but keeping the O2 percentage should be fine. Going to 1.5 ATMs and keepting the O2 percentage is alright, but probably not ideal. Going to 2 ATMs but reducing O2 to (say) 15% (meaning 0.3 bar PP) is fine.
Of course, there are some caveats.
This is based purely on short term testing. We haven't seen what happens to someone who lives a lifetime in 0.5 bar PP O2 and my guess is that over time some long term factors could come into play. Generally speaking O2 is a key chemical in releasing energy in our bodies but it also appears to play a critical role in our ageing process. This is why antioxidants are so popular as a health supplement. It's possible that at 0.5 bar, people could operate with more energy, be more agile, faster runners et al but eventually live a shorter lifespan as a result. We just don't know yet.
Also, what I've been describing is the effect of O2 PP on humans. If you have creatures that have evolved in higher PP levels of O2, then you would expect them to have metabolisms and physiological structures (like perhaps smaller lungs) to cater for this change.
Also, if you have a natural fear of insects, then you don't want to live on such a world. Insects don't have lungs and rely on O2 absorption through their carapaces saturate their bodies with O2, meaning that the PP of O2 places a limit on how big they can grow. More O2 in the atmosphere, the larger they can grow.
Finally, if you keep the atmospheric composition similar to Earth's but just increase the pressure, swapping out excess O2 PP for more Nitrogen, you run into a completely different problem. Once you reach about 3 ATMs, the nitrogen PP is sufficient to trigger a narcotic effect. Continuing to increase it ALSO leads to toxicity. Modern scuba divers know this and often have to dive deeply with special air mixes that reduce both O2 and N2 so that neither have these effects. It should also be noted that such a high pressure means that your CO2 scrubbing systems would have to be VERY efficient; preferably a very high concentration of vegetation to animal life on such a high density atmosphere planet. Why? Well that same issue with PP also means that at 3 ATMs, CO2 concentrations start to become a problem at around 0.35%.
So; if you're designing a dense atmosphere, O2 is certainly a consideration, but it's not the only one. Your best starting position is researching scuba air mixes for deep dives, then using that as a starting point for your density calculations in terms of PP and what other gasses you could use to thin the air out a little, so to speak.