yes, you can do this. You just need to add both controllers into same mobility domain if you require client to roam between APs in these two controllers.
Keep in mind having same software code on both controllers is recommended. Otherswise if AP fail over it has to downgrade/upgrade which cause longer outages for wireless users.
44xx only support upto 7.0.x & you have to keep 5508 in that version if you want to keep both WLCs
I would go for 5508 with sufficient license & retire the 44xx rather keeping old WLC software
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