This is exactly what the HSB colour model is for. HSB splits the colour into the values
Hue (H), or colour type;
Saturation (S), or (inverse) amount of white in the colour; and
Brightness (B), (inverse) amount of black.
Hue is expressed in degrees, with 0° being red, and 180° being cyan.
Saturation and Brightness are expressed in precentages. 0% Saturation is just white, no colour, and 100% is no white, just the colour. 0% Brightness is all black and 100% brightness has no black left mixed in.
Any current design program has a colour picker that includes the HSB (or HSV) model. Pick the colour you want alternatives for, and play around with its S and B values. As a rule of thumb, decrease saturation for a lighter variant and decrease brightness for a darker one.
All these variants harmonise with your base colour naturally.
The HSB model is a great base to build entire colour palettes on, using only a few values of H and creating variants of those with S and B. If you use colour theory to choose your base values of H so they harmonise, then their variants created by changing S and B will also harmonise with each other.