In the ‘Student Resources – Basic’ there are some frequently asked questions culled from the old forum. The 4th question concerns the situation you describe here.
There are other possibilities. If you have the ‘advanced’ membership, there’s a section on that resources page about chord substitution that may provide some opportunities. Keep in mind that you’re determining a ‘target’ chord and then figuring out ways to get there.
In some situations a simple approach that may work is taking the chord that follows the major and use it as the second chord of the measure with the major and then repeating that sequence for the second chord. In other words, instead of a major for a full measure followed by a m7th for a full measure, play |M m7 | M m7 |