Not too hard
I don't think this is a big challenge.
There are a couple of ways to go about it, that I can think of now. The 2nd method requires a sound module that can play multiple layers at a time.
First, just to make sure we are on the same page, a Sequence is a program of a song that plays back the same way each time you hit the play button. So, just want to make sure that I'm approaching your wish the correct way.
Apparently, you wish to write/record a song that has particular pitches in it, that are not 1 of the 12 tones in the octave.
Since you want access to more than 12 tones in an octave while a sequence is firing, the suggestion of the pitchbend will do just fine. You probably just are unaware of how to program the spec. It's not too hard.
In fact, if I search this forum, I think this has been addressed before, elsewhere. Goes something like this: The MIDI parameter that adjusts pitchbend is plus or minus 9600. (Can't remember exactly, but it's easy enough to search). So, prior to the note you want played (the strange pithed note), you insert the pitchbend spec and the note will play back at whatever pitch you want.
You just have to make sure your have another pitchbend command after that note to reset your scale back to default, or else all the notes following will go off.
Takes some experimentation, not too much, but this is really an easy way to do it.
The 2nd way I can think of, is even more flexible, and powerful... is depending on how many strange pitched notes you desire, you can have multiple layers of sounds (you probably want the same sound on each layer), and then detune each layer by the amount of cents you desire. This method works, provided that all your "strange" pitched notes you desire are constant/consistent. Always, say, 30 cents off from the tonic, in either direction.
100 cents per half-step, i.e. between C and C#.
So, 1 layer is normal, the 2nd layer is off by 20 cents (1/5 detuning), the next layer 30 cents (3/10 detuned), etc.
But you need powerful equipment to use this 2nd method, i.e. Kurzweil workstation, or Maybe Reason's sampler. The reason I state this is because some keyboards force all layers to be detuned when you adjust the cents parameter. And that will not do for your need. Kurzweil allows you full control over every single thing you want to put your mind to.
Now, your sequencer has to know which note and layer to fire upon, and it will do just fine.