My data set has 60 participants. Data was collected from each of them 3 times over seven months, and at each time, each participant did two types of speaking tasks (monologic and dialogic). So my spreadsheet has 360 rows (60 participants x 3 times x 2 tasks each time=360). The dependent variable is proficiency scores (each participant took a proficiency test at each time. So I have 60x3=180 proficiency scores).The fixed factors are the linguistic variables derived from the monologic and dialogic speaking tasks that the participants did at each time. I am building Linear Mixed Effects (LME) models on R to examine:

1. whether the relationship between the linguistic predictors (fixed factors) and the proficiency scores (dependent variable) varied depending on the speaking task-type (monologic/dialogic) and
2. whether the relationship between the linguistic predictors (fixed factors) and the proficiency scores (dependent variable) varied depending on the time (time 1/time 2/time 3).

My question is how many fixed factors can I enter in each LME model? I need to include task, time, and text-length(to control for the confounding effect of the amount of speech produced) as fixed factors in each LME model. But apart from these 3, how many fixed factors can be entered in each LME model? I am aware that in linear regression models, the rule of thumb is 1 predictor per 10 observations. Does this also apply to LME? If yes, am I allowed to include only 6 predictors in each LME model? I would appreciate any help. Thank you very much.