I guess you are talking about Tahiti Limes ? Or is that West Indian / Key Limes ??
There are different clones of both of these which might make a difference in flowering season.
Italian Lemon growers manipulate the trees growth to get multiple crops.
Not sure if this could be done with Limes. Obviously you need to induce flowering.
Stress can be used to induce flowering in Citrus, i.e. reduced irrigation. Cincturing might also help ?
Fertiliser applications may promote flowering. Different Citrus rootstocks may slightly extend the season.
You could check out Italian Feminello Lemon production techniques.
http://citruspages.free.fr/lemons.php#femminellotranscript below
Femminello forms a group of several lemon selections each with its own characteristics (see at the bottom). All Femminello lemons are vigorous, productive, ever-blooming and ever-bearing. Femminello is the most important lemon variety of Italy. Collectively they form about 75% of Italian lemon production.
Femminello is a medium sized tree with few or no thorns. In suitable conditions it flowers almost around the year. In Italy Femminello trees are regulated by irrigation and fertilization to produce six crops per year. The harvests and their fruit have different names:
Marzani blossom in February-March and mature the following January-March
Limoni invernali blossom in March-April and mature November-March
Bianchetti blossom in June-July and mature following April-June
Verdelli blossom in July and mature following July-September
Primofiore blossom first in March and mature in September-November
Bastardi blossom in autumn and mature in the autumn of the following year.